'"^>«^ , V- <3 =51 * y>A ^ ■?- <:3 C3, * 





-.% 



•,- ^ c> -f ^.^ ^ r- ><? =51 •» ^.X^ 



^ %^^^ 




'%^^ 



3 ^ 









-d 



^o:y,f^,. 





V ^^<._ .^ 







*"oo^:o-^.>. 



-d< 








rju o 












c?^^^^^^^ ^ ^'J^m. 










-^.^^ 



^t- 



s .r*-' 



# % '- ' 



t?> 









C>\^ 



^ .r.^" 






^% "'^<^^V""^^^° -^ 




-^/.o^ 






- .r^ 






<^ 










w 










^MILIAR XECTURES 



NATURAL PHILOSOPHY 



USE OF SCHOOLS 



By Mrs. A. H. LINCOLN PHELPS, 

Author of Familiar Lectures on Botany, Chemistry, Botany and Geology for 
Beginners, Female Student, &c. 



NEW-YORK: 

PUBLISHED BY P. J. HUNTINGTON AND CO 
174 PEARL-STREET. 

1837. 



ac 



\%^ 



F. J. HUNTINGTON AND CO. 

HAVE EECENTLY PUBLISHED 






Familiar Lectures on Botany, Practical, Elementary and Physiological, 
with an Appendix containing descriptions of the plants of the United States, 
exotics, &;c., for the use of private students and Seminaries, by Mrs. Almira H, 
Lincoln, late Vice Principal of the Troy Female Seminary. Fifth Edition, re- 
vised and enlarged. 

Also by the same Author^ 

Botany for Beginners : Introductory to the above work, and designed for the 
use of Common Schools, and the younger pupils of Higher Schools and Acade- 
mies, by Mrs. A. H. L. Phelps, (formerly Mrs. Lincoln.) 1 vol. 18 mo. pp. 156. 
„ Chemistry for Beginners. Same size as the! ..st named work, and designed 
aa an introduction to a work now in 

PREPARATION for THE PRESS, 

Familiar Lectures on Chemistry, for Schools and Academies, in 1 vol. 12 
mo. with numerous engravings. 

Also, nearly ready for the Press, by the same Author, 
Philosophy for Beginners, designed as an Introduction to the Familiar 
Lectures on Philosophy, same size and price as the Botany and Chemistry for 
Beginnersi 



Entered according to Act of Congress, in the year 1837, by 

F. J. HUNTINGTON, 

In the Clerk's Office of the Southern District of New York. 



p. CANFIELD, PRINT. HARTFORD. 



/>?¥ 



■n- 



PREFACE. * 



The author has adopted the style of familiar address, because, 
while equally favourable for the communication of knowledge, it is 
more interesting to the pupil than a formal didactic style. A 
main feature in her manner of treating the subject, consists in 
bringing forward facts of common occurrence, to illustrate prin- 
ciples ; thus teaching the young to reason for themselves- 

Various authors have been consulted; and in many cases the 
lemguage of other writers has been adopted, especially when an 
alteration would not have been an improvement. To paraphrase 
an author's ideas, for the sake of an apparent originality, is as 
unwise as it is dishonest 

This work, though based upon the labours of the learned, is 
not a mere compilation. — The author has endeavoured to invest 
the subject with something of freshness and interest, that may- 
enliven the progress of the young, as they climb the hill of sci- 
ence. We have sometimes paused on our way, to discourse of 
Him who formed the world, and from whose eternal mind the 
laws of physical science originated. — Our hearts have been 
warmed and animated with thoughts of the wisdom and good- 
ness which irradiate every page of the volume of nature. 

American parents and teachers ; to aid you in your duties, to 
benefit the beloved objects of your care, I have laboured to pre- 
pare this volume. I commit it to you, in the confidence that 
while it shall impart to your children and pupils, the principles 
of science, it will at the same time exert a salutary influence on 
their moral and religious affections. 

In the attempt made in this, and other works, to connect with 
the study of the sciences, religious thoughts, I find myself sup- 
ported by that profound and philosophical writer, Madame Neck- 
er De Saussure, from whose second volume on Progressive Edu- 
cation, the following is an extract. " Religion alone unites and 
connects the various departments of education, external objectis 
with the affections of the heart, the laws of physics with the 



Vi PREFACE. 

laws of miiid; it is the inflaenceof religion only which can cause 
science and duty to meet in the same point. What relation^ 
merely human, could we, for example, find between two subjects 
in appearance so foreign from each other, as those of physical 
phenomena, and the moral obligations imposed on man ? and yet 
a connexion exists ; they have one common source. One God, 
the sovereign legislator of nature and tlie soul, wills the reign of 
universal order. He has subjected matter to the laws of an irre- 
sistible necessity, and he has imposed on the free agent, man, 
a necessity which, though it appears less imperious, forces 
his will b}- bitter experience of the evils attached to a neglect of 
duty. When the creations, and laws of one discerning mindy 
present themselves on every side, and in the government of the 
universe^ numerous relations are seen to exist between the difier- 
ent departments of knowledge. To the subjects most fitted to exer- 
cise the talent of investigation inherent in the mind of man, are 
connected objects which appear chiefly fitted to his physical 
wants, and even those which seem created but to please his ima- 
gination. If God is the eternal geometrician^ who has calcu- 
lated with exactitude the measure of the different forces in the 
universe, if he is the icise legislator who has engraven his lass's 
upon our souls, if he is the supreme artist, who has spread forth 
beauty upon the earth and in the heavens, and has rendered us 
sensible to its charms ] and as there is nothing in the physical 
world which is not the immediate work of God, and nothing in 
the moral world, which does not result from faculties with which 
he has endowed man, there can be neither object nor thought, 
w^hich may not be connected with God. Thus all may be linked 
together, all may harmonise ; ideas, before insolated, unite in the 
mind of the pupil ; he views creation as a whole ; — and as soon 
as he perceives the unity of design in nature, his reason, 
though still feeble, presents some resemblance to the Supreme 
reason which conceived the design.''^ 



MRS. EMMA WILLARD, 

THIS VOLUME IS AFFECTIONATELY 

AND GRATEFULLY DEDICATED, 

BY HER SISTER, 

ALMIRA a L. PHELPS. 
Brattlebor^gh, Vt. June 1, 1837. 



ERRATA. 

V 99, last line, read, '• as the square orthe distance from the centre incrftasea." 
f 100, read, the attraction of the earth at the moon is 3500 times less than at 

the earth's surface, 
T 169, second line, after "set" read it. 
« 298, first line, for "see 87" read, see 86. 

IT 489, fourth line from the close, for " to not always" read, is not always. 
H 674, last line, for D B F read, B D P. 
Note 10 Tf 710, read, producing the line P C to Q,, the angles Q, C Pand P 

C E being vertical. 
If 720, at tiie eleventh line, for '* reflection" read, refraction. 
f 738, last line but one, for "rates" read, ratio. 
« 794, for "magnifying mirror" read, magnifying jjotper. 
* 821, for "caryta" read, barijta, 
« 917, for "areas" which subtend, read, arcs which subtend. 



Note. — Teachers who, in using this work, may discover any imprartaBt er- 
rors, are respectfully requested tci communicate the same to the author, with any 
suggestions which nxay produce improvements in future editions. 



CONTENTS 





PART I. 






OF MATTER AND ITS MECnANICAL PROPERTIES. 


rAOK. 


LECTURE 1. Introduction; or the objects and advantages of Science, 13 


IC 


11. or Abstract Science. Geometrical definitions, 


20 


« 


Iir. or the Properties of Matter, 


26 


« 


IV. Gravity, .... 


37 


(( 


V. Moti.)n and Force, 


46 


C( 


VI. Of the Laws of Motion, . 


52 


IC 


VII. Compound Motion, 


CO 


(( 


VIII. Acceleroted and Retarded Motion, 


67 


« 


IX. Curvilinear Motion. Projectiles, 


75 


u 


X. Centre of Gravity, 

PART II. 

OF THE MECHANICAL POWERS. 


83 


LECTURE XI. Machines. The Cord. The Lever, 


98 


«( 


XII. The Lever continued. 


101 


(( 


XIII. The Inclined Plane, 


103 


" 


XIV. The Pulley, .... 


111 


(C 


XV. The Wheel and Axle. The Wedge. The Screw, 


116 


I( 


XVL Friction. Moving Povirers. General remarks upon 




Machinery, .... 


123 


it 


XVII. The Pendulum, 


I3a 


u 


XVin. Locomotion, , 

PART III. 

HYDROSTATICS. 


13a 



LECTURE XIX. Mechanical Properties of Liquids, 
" XX. Pressure of Liquids, 

" XXI. Specific Gravity, 

" XXIL Hydraulics or Liquids in Motion, 



145 
149 
161 
171 



PART IV. 



PNEUMATICS. 

LECTURE XXIII. .Piriform Bodies. Atmosphere. The Air, 

" XXIV. Properties of Air, . . . . 

" XXV. The Condensation of Air. Condensing Syringe, 

Artificial Fountains. Air Gun. Diving Bell, 
" XXVI. Barometer. Eifect of Heat upon Air, . 

" XXVIL Winds— Their Causes and Effects, I 



176 

18a 



194 
200 



VI 



CONTENTS. 



LECTURE XXVIII. Meteorology. Steam. Elastic Force of Steam. 

Stcatn Engine, . . . .212 

" XXIX. Atmospheric pi essure upon Water. Pumps. Syphons, 221 

PART V. 



ACOUSTICS. 

LECTURE XXX, Sonorous Bodies. Bells. Musical Strings, ^olian 

Harp, . . . . .227 

" XXXL Medium of Sound. The Ear. Echo. Speaking 

Trumpet. Velocity of Sound. Music. The Hu- 
man Voice, ..... 233 

PART VI. 

OPTICS. 

LECTURE XXXII. Light. Definitions. Motion of Light. Its In- 
tensity. Of Reflection, Refraction and Inflection, 247 
" XXXIII. Reflection from Mirrors. Plane Mirrors. Con- 

vex Mirrors. Concave Mirrors, . . 254 

XXXIV. Refraction of Light, , . .274 

XXXV. Lenses, , . . . .286 
" XXXVI. Visual Angle. Pore-Shortening. Perspective. 

Intensity of Light and Shade. Convergence of 
the Optic Axes, ... - 294 

" XXXVIf. Dm-ation of Impressions upon the Eye. Single 

Vision. Imperfection of Vision. Optical 
Instruments. Shadow, . . . 306 

" XXXVIII. Nature of Light. Decomposition of Light. Dis- 

persion of Light. Rain-bow. Absorption of 
Light, . . . . .319 

PART VII. 

ELECTRICiry ATs'D JIAGNETISM. 

LECTURE XXXIX. Theories of Electricity. Mode of obtaining Elec- 
tricity. Conductors and Non-concluctors. Elec- ♦ 
tricul Apparatus and Experiments illustrating 
the Nature of Electricity, . . . 330 

" XL. Atmospheric Electricity, . . .341 

" XLI. Magnetism. Inclination of the Magnet. Declination 

of the Compass, .... 345 

PART VIII. 

CELESTIAL MECHANICS, OR ASTRONOMY. 

LECTURE XLIL Introd'ictory Remarks, Armillary Sphere. Imaginary 
Circles. Tlie Solar Sj-stem. Planets. Comets. Ap. 
plication of Miichaaical Laws to Planetary Motion, 355 
•* XLin. The Fixed Stars. The Constellations. Galaxy. 

Nebulae. Coaclusiun. . . . Z$9 



FAMILIAR LECTURES 

ON 

NATURAL PHILOSOPHY. 



PART L 

OF MATTER AND ITS MECHANICAL PROPERTIES. 



LECTURE L 

INTRODUCTION. 

OF THE OBJECTS AND ADVANTAGES OF SCIENCE. 

1. At the, commencement of a new study, we naturally 
desire to know something of its objects and advantages. 
Natural philosophy recommends itself to attention for its 
injluence on the mind, and for its practical utility. 

2. First, The habit of study is of great importance. 
No one can ever arrive at eminence, or indeed be well pre- 
pared for the ordinary duties of life who cannot fix his mind 
steadily upon a subject and follow out a train of reasoning. 
Such studies as require close reasoning, and consecutive 
thinking, are to be recommended for their influence upon 
the mind apart from their other advantages, Among this 
class of studies, none holds a higher rank than Natural 
Philosophy. Some pupils who have more talents than in- 
dustry, will manage to get through a recitation in geography 
or history with little previous study. By means of a cer- 
tain fluency of speech, and some confidence, they may make 
out to say something that will pass off very well. But, in 
the study we are now entering upon, the pupil must under- 

Fiist advantage of the study of Natural Philosoiiliy. Studies best ada[ite(l 
to strengthen the mind, 

•2 



14 NATURAL PHILOSOPHY. 

si.and his lesson or he cannot recite it. Tliis should not dis- 
courage you. No young person desires to be either weak 
minded or superficial ; and, that this may not be the case each 
one should apply himself to such pursuits as will strengthen 
his mind and invigorate his understanding. If one were to 
confine the hand of an infant so that he could never use it, 
it would be weak and powerless ; and it is thus with the 
mental faculties, if we would have them strong and active, 
we must use them. 

3. Second, The love of knowledge is a principle of our 
nature. To feel ourselves becoming wiser, more assimi- 
lated to the great minds which have instructed mankind, 
and better able to see the plan and harmony of the creation, 
seems to add a new dignity to our own m.inds. There are 
in such feelings and perceptions, enjoyments which must be 
vainly sought for in amusements which neither elevate nor 
refine our nature. " He who is accustomed to trace the 
operation of general causes, and the exemplification of 
general laws," says Herschel, "vralks in the midst of won- 
ders unknown to the ignorant, and unseen by the unenquiring 
eye ; every object that falls in his way elucidates some prin- 
ciple, affords some instruction, and impresses him with a 
sense of harmony and order. Nor is it a mere passive 
pleasure which is thus communicated. A thousand ques- 
tions are continually arising in his mind, a thousand subjects 
of enquiry presenting themiselves, which ket-p his faculties 
in constant exercise, and his thoughts perpetually on the 
wing, so that lassitude is excluded from his life, and that 
craving after artificial excitem.ent and dissipation of mind, 
which leads so many into frivolous, unworthy and destruc- 
tive pursuits, is altogether eradicated from his bosom," 

4. Third, Knowledge is power. It is this that gives to 
civihzed man his advantage over the savage. It is know- 
ledge which guides the arts that minister to the comfort of 
domestic life, directs the mechanic in the fabrication of arti- 
cles of convenience and luxury, and presides over the opera- 
tions of war. It has been said, that " if a man have but a 
pot to boil, he may learn from science lessons that will 
enable him to cook his morsel better, save his fuel, and both 
vaiy his dish and improve it." A knowledge of the princi- 

Pieasures of knovrle Ige. Usefulness of knowledge. 



INTRODUCTION. 15 

pies of science not only renders the rsian who labours for his 
bread more skihlil and expert in liis occupation, but gives 
him an opportunity of making improvements in the arts at 
which he works, and new discoveries in philosophy 

5. Fourth, The study of nature leads us to a more inti- 
mate communion with the Great Author o^ Nature. We fol- 
low his footsteps, we behold the works of his hand, and v/e 
learn the laws by which he governs the material world. 
What pursuit can be more noble, what better fitted to engage 
the attention and delight the heart of the philosopher and 
christian ? 

6. The term philosophy means a knowledge of the rea- 
sons or causes of things. A. knowledge of these causes leads 
to important inventions. Every one is familiar with the fact, 
that the lid of a tea kettle is forced upward v/hen the water 
is boiling violently within it : yet, perhaps, some persons 
grow old without ever thinking why this should take place. 
An observing mind, while reflecting upon it, Vv'ould perceive 
that water acted upon by heat, passes into steam or vapour, 
which, by its expansive force, raises the lid of the kettle. 
Having ascertained this power of steam, he might then 
imagine how it could be applied to machinery, and thus pro- 
ceed to invent a steam engine. By similar steps have pro- 
ceeded those, who by their bold inventions, have subjected 
the powers of nature — fire, water, and wind — to the controul 
of man ; and thus contributed to the comfort and prosperity 
of society, and enrolled themselves among the benefactors 
of mankind. 

7. Philosophy is of various kinds, as Mental Philosophy, 
which enquires into the faculties of the human mind ; and 
Moral Philosophy, which investigates the principles of mo- 
rality or duty. We speak also of the philosophy of Gram- 
mar, of Rhetoric, and of the Philosophy of the Bible ; mean- 
ing the consideration of their general principles. 

8. The Philosophy of Nature, usually called Natural 
Science, has a more extended signification than Natural 
Philosophy. The former includes Chemistry, which con- 
siders ths elements of substances, and Natural Plistory, which 
observes 1\\q\v forms and external organs, as Mineralogy, 



Effects of the study of nature upon the mind. Philofophy. Difference be 
tweeu the philosophy of nature and natural philosophy. 



16 NATURAL PHILOSOPHY. 

Botany, and Zoology. Natural Philosophy takes a different 
view of the same object ; matter in all its various forms, 
constituting animals, plants, rocks, earth, air, water, &c. &c. 
demands the attention of the student in all these sciences ; 
but it is inorganized matter only, or that which is not influ- 
enced by a living principle that comes within the depart- 
ments of Chemistry and Natural Philosophy. The two lat- 
ter sciences may be considered as bearing a relation to each 
other like that of the microscope and telescope ; the one 
looks at objects near by, and scrutinizes their minutest parts, 
while the other takes a more general survey, and operates 
upon a much broader scale. 

9. Some knowledge of all the sciences which explain the 
material world, is of great importance to the young. It is 
therefore very difficult to point to any one and say, *' this is 
the most important study," or even to decide which of the 
sciences should receive the earliest attention. It is certain 
that attainments in any one branch of natural science, facili- 
tate the study of the rest. They form a circle of most in- 
teresting and important knowledge, and it is unessential 
when the pupil commences if he do but compass the whole. 
In the study of Natural Philosophy, besides the advantages 
which may be expected in cultivating the powers of memory, 
reasoning, and observation, the mind will be enlarged by new 
views of that Infinite Wisdom which has so nicely balanced 
the powers of nature, that all material things, whether 
atoms, systems, or worlds, are retained in their proper places, 
even by the very action of forces which tend (as it might 
seem), to draw them in opposite directions. 

10. The A-lmighty Creator hath brought into existence 
two very different classes of substances, Mind and Matter. 
Every thing which we know, or of which we can conceive, 
belongs to one or the other of these great divisions. There 
must be one Being in the universe who has always existed, 
because neither mind nor matter produced in time could 
have created itself This self- existent, uncreated Being, the 
Author of all things, is God. 

11. In our own persons, mind and matter are connected 
by a common tie which we call life. The brute creation 



Natural philosophy and chemistry compared. Circle of the sciences. Ar- 
gument for the existence of a Creator. 



INTRODUCTION. 



17, 



have a lower order of mind called instinct, by nneaiis of 
which they acconnplish their distinct ends. Plants have a 
living principle, but are incapable of action. A stone, a 
piece of wood, water, air and light, are matter uncombined 
with mind, they have neither soul nor instincts, and possess 
no principle of life. 

12. The study of matter with respect to its general pro- 
perties, and the laws hy luhich it is governed, constitutes Na- 
tural Philosophy. 

13. This science is founded on observation and experi- 
ment, that is, nothing is received as fact which is not the 
result of careful and attentive observation, and which may 
not be proved by actual experiment. 

14. Matter is the subject of the science, and Mind the in- 
strument by which its operations are carried on. By means 
of the senses which are themselves subjected to the will of 
the soul or mind, the latter becomes acquainted with objects 
external to itself. 

15. We may then define matter to be that which acts 
upon any of our senses ehhev immediately or by means of 
its effects on other bodies. Each of the senses gives in- 
formation of certain properties of matter, the existence of 
which we could never have learnt from any other source. 
To the sense of touch or feeling, we owe our ideas of the 
softness or hardness and the length and breadth of bodies. 
Sight gives us ideas of colour, the varieties of which, as we 
shall learn hereafter, are produced by the reflection of dif- 
ferent rays of light. Without this sense, we could have no 
conception of the effects of light as seen in a picture, rain- 
bow or cloud. We might, from feeling, learn to distin- 
guish a square from a sphere or a cylinder, and acquire 
general notions of figure and extension, but could never 
have any idea of the variety of forms which are presented 
in a natural landscape, where rocks, trees, brooks, and mea- 
dows are grouped together in a picturesque assemblage. A 
blind person might, by feelir)g, gain some idea of the magni- 
tude and figure of a church, but he could have no concep- 
tion of the beauty of architectural proportion, or the general 
appearance of the building. 

Distinctions in the creation. What is natural philosophy? Ou what found- 
ed ? How docs the mind learn the properties of luattn ? Definitions of rmutcr. 
Touch and sight. 



18 NATURAL PHILOSOPHY. 

16. When, on entering an apartment, or walking in a 
garden, we perceive the odour pecuHar to a rose, we believe 
this flower to be near us ; when we hear a flute or a gun, 
we believe in the existence of an instrument which caused 
the sound. And should any one tell us that the odour and 
sound proceeded from nothing, we should know this to be 
false. 

17. The causes of all our various sensations we call mat- 
ter. Our reference of the sensations to its cause, we call 
perception. When a person says, "I smell a rose," he 
means that he perceives by the odour that there is a rose 
near. Taste, though a sense from which we derive many 
pleasures, and by means of which social enjoyment may be 
promoted, seems less important as a means of acquainting us 
with external things than the other senses, since what we 
taste we can also see, touch and smell. 

18. You will observe that the properties, and not the es-. 
sence of matter, are the proper objects of philosophical en- 
quiry. We will explain this : — suppose you enquire what is 
an orange ? we tell you it is something which is of a round 
figure, a yellow colour, has an agreeable odour, and pleasant 
taste ; but we have yet only enumerated qualities or properties 
of the orange; and though we might go on and mention how it 
grew from a seed, and explain the whole process of vegeta- 
tion, still we should not have answered the original question, 
" what is an orange '/" if we consider this as referring to its 
essence. Indeed such enquiries are beyond the limits of our 
faculties ; though in past ages they were vainly pursued by 
philosophers who sought rather to perplex men by hypothe- 
ses, than to enlighten them by actual discoveries of truth. 

19. It is now admitted that mankind must be satisfied 
with making the best possible use of such knowledge of 
matter as they can gain by their senses, without attempting 
to form theories on subjects beyond their reach, or "to 
draw on their imagination for facts." The soul within its 
dark prison can look out upon external things but through 
those kw avenues, the senses ; we are not, however, to sup- 
pose that they reveal all, or indeed but a small part of the 
creation. With a sense of discerning the spiritual exis- 

Sraell and hearing. Perception. The proper objects of philosophical en- 
quiry. We are dependant on the senses for a knowledge of things external. 



INTRODUCTION. 1 9 

tences which surround us, what glorious images would be 
at once revealed — even God himself: and, it may be, the 
spirits of departed friends, anxiously observing our con- 
duct. 

20. But limited as human faculties are in this world, which 
is but the threshold of existence, they can yet accomplish 
much by observing, comparing, and experimenting upon 
such properties of objects as they have the power to per- 
ceive. Thus the blind could not by any expedient be 
made to see the forms of letters impressed upon the printed 
page, and it would be useless labour to attempt to teach them 
to read in this manner ; but by means of raised characters 
which they can learn to distinguish by touch, they may be 
instructed. Wherein then our Creator has withheld from 
us light, let us humbly acquiesce in our blindness, while we 
honour him and promote our happiness by making the best 
possible use of the faculties with which he has endowed 
us. 

21. In the beautiful language of an English writer,* the 
character of the true philosopher is to hope all things not 
impossible, and to believe all things not improbable. He 
who has seen obscurities which appeared impenetrable, in 
physical and mathematical science, suddenly dispelled, and 
the most barren and unpromising fields of enquiry convert- 
ed, as if by inspiration, into rich and inexhaustible springs 
of knowledge and power, on a simple change of view, or by 
merely bringing to bear on them some principle which it 
never occurred before to try, will surely be the very last to 
acquiesce in any dispiriting prospects of either the present or 
future destinies of mankind ; while, on the other hand, the 
boundless views of intellectual and moral, as well as mate- 
rial relations, which open to him on all sides in the course 
of these pursuits, the knowledge of the trivial place he oc- 
cupies in the scale of creation, and the sense of his ov/n 
weakness and incapacity to suspend or modify the slightest 
movement of the vast machinery he sees in action around 
him, effectually convinces him that humility of pretension, no 

Sir John Herschel. See "Preliminary Discourses on Natural Philoso- 
phy." 



Our limited faculties no excuse fur mental inactivity. Character of the true 
philosopl er. 



2y NATURAL PHILOSOPHY. 

less than confidence of hope is what best becomes his char- 
acter. To the natural philosopher there is no natural ob- 
ject, trifling or unimportant. Fix)m the least of nature's 
works he may learn the greatest iessons. The fall of an 
apple to the ground may raise his thoughts to the laws which 
govern the revolutions of the planets in their orbits ; or the 
situation of a pebble may afford him evidence of the state of 
the globe before his species became its denizens. And this 
is, in fact, one of the great sources of delight which the 
study of natural science imparts to its votaries. A mind 
which has once imbibed a taste for scientific enquiry, and 
has learnt the habit of applying its principles readily to the 
cases which occur, has within itself an inexhaustible source 
of pure and exciting contemplations ; such a man finds 
" tongues in trees — books in the running brooks — serm^ons 
in stones — and good in every thing." 



LECTURE 11. 

OF ABSTRACT SCIENCE. — GEOMETRICAL DEFINITIONS. 

22. There is a great difference between natural science 
and abstract science. Natural science is the knowledge of 
thmgs, o^ causes and iheir effects ; or in other words, of the 
laws of nature. Abstract science is the knowledge of signs, 
as of language, or of numbers, as in arithmetic and algebra ; 
it is also the study of independent truths, which relate lo 
space and extension, as in geometry, and all subjects which 
are capable of accurate demonstration. 

23. Some acquaintance with the powers of language is 
necessary towards the comprehension of any science ; and 
the more thorouo^h and extensive is one's knowledge of 
words, or the signs used to convey ideas, the more readily 
he comprehends the teachings of others, and the more easi- 
ly and accurately he can communicate the results of his 
own thoughts. 

DifFerence between natural and abstract science. A knowledge of language 
important. 



GEOMETRICAL DEFINITIONS. 21 

24. The learner in Natural Philosophy should have sonne 
acquaintance also with the elennentary principles of mathe- 
matics ; the knowledge of its truths depend jnore on reasoning 
than observation. Thus, though there might not exist in space 
such a real thing as a triangle, yet when we see one marked 
out before us, and are told that the sum of the three angles 
are equal to two right angles ; and when this is proved to us 
by a train of geometrical reasoning, we cannot refuse our 
assent to the truth of the fact of the existence of the three 
angles in a triangle, and that they are equal to two right 
angles. 

25. Upon a few simple truths involving space and num- 
bers is built the noble science of Mathematics. Beginning 
with these truths, Euclid, more than two thousand years ago, 
erected, from materials furnished by his ov/n reason, an edi- 
fice which succeeding mathematicians have neither been 
able to overthrow nor improve. Ancient philosophers 
thought they miglit in the same abstract independent man- 
ner, by the mere strength of their own reasoning, establish 
systems of philosophy equally invulnerable to the scrutiny 
of truth and of time. But it was soon found that although 
the human mind was capable of penetrating and solving 
those truths and consequences involved in ideas of number 
and space ; yet it could never, by any effort of mere reason- 
ing, learn that a lump of sugar would be dissolved by water, 
while a piece of marble would remain unchanged in the 
liquid. The progress of the physical sciences was long 
obstructed by the blindness of the learned to the true mode 
of scientific investigations. As soon as philosophers began 
to understand that the only v/ay of learning the laws of na- 
ture was to observe natural phenomena, and consequently 
began to substitute enquiry for hypothesis, discoveries were 
made and principles established. Thus, while true science 
aims to penetrate and unfold the deepest mysteries of nature, 
she despises not the humblest and most simple means of ob- 
taining her object. 

Mathematical truths learned from reasoning rather than observation. Error 
•-^f ancient philosophers. 



22 



NATURAL PHILOSOPHY. 



Geometrical Lines and Figures. 

26. As the science of natural philosophy derives much 
assistance from geometry, it is necessary that the pupil 
should become acquainted with those geometrical lines and 
figures, which will occasionally be introduced in our illus- 
trations. 



/ ^\ 27. A circle \s a perfect figure contained by 

le circumference or 
lere equally distant 
the centre. 



027. A circle is a perfect fi 
one line, which is called the 
periphery^, and is every whe 
from a point within, called th 



28. Radius is a strait line from the centre 
of a circle to its circumference. The plural 
of radius is radii. Radii of the sam.e circle 
are equal to one another. 



29. The diameter of a circle is a strait line 
drawn through the centre, and terminated on 
both sides by the circumference, it is twice the 
radius, and divides the circle into two equal 
parts called semicircles. | 



29*. QuadrantX is half a semi-circle, or a 
quarter of a circle. 



' Periphery is from the Greek j^e;?", aixund, &xAr,]tero,\0 carry, meaning to 
surround tlie circle. 

t ^etni, Irorii the Gi-reek, signifying half. 

+ Quadrant, from the Latin qixadrwut, signify'ino a fouith fait. 

Why is some knowlfdge of geou.etrical lines and figures neccrsary in study- 
ing natural fhibsopby 1 



GEOMETRICAL- DEFINITIONS. 



23 






30. A chord is a right line which cuts tlie 
g circle into two equal or unequal parts. The 
lines A B and B C are cliords. 

31. Arch^ or arc of a circle is any part of 
. the circumference ; the figure contained by a 
strait line, and the arc of a circle is called a 
segment. 

32. Sector (a) is the figure included be- 
tween two radii, and is less than a quadrant. 
Tangent (b) is a rightf line touching a curve^ 
but not cutting it. 



33. Every circle, large or small, is sup- 
posed to be divided into 360 degrees, marked 
on the circumference. A semi-circle is 180 
degrees, and a quadrant is 90 degrees. Each 
degree is divided into 60 equal parts, called 
minutes, each minute is divided into 60 equal 
parts called seconds. 



34. Parallel lines are strait 
lines, equally distant from each 
other in every part ; and if extended to an infinite distance, 
would never meet. 

35. Lines not parallel, but in- 
clining towards each other in the 
same planef must, if sufRcientlv 
produce^!, meet somewhere, and 
thejDoint where they meet is called an angle, or corner, as 

* Pronounced ark. 

t A rig/U line, ia goon'.etr}-, means the same tliiiig as a slraight line, 

's B\- p!(ine is in':-ant a level surface, ox- i^lain in common hiugu.ige. 




24 



NATURAL PHILOSOPHY, 



at A ; or an angle may be defined an opening made by two 



straight lines. 



"D 36. When one line meets or 
crosses another line perpen- 
dicularly, at their point of 
contact they form a right 
angle ; thus the perpendicu- 
lar line A, in crossing i he 
horizontal line C D, forms two right angles at B and E. A 
right angle is a square corner ; it is also an angle of 90 de- 
grees, for if included within an arc of a circle, it forms a 
quadrant. 




37. Half a right angle is an angle of 
45 degrees. Any angle less than a right 
angle is called an acute or sharp angle, as 
at A. An obtuse angle is greater than a 
right angle ; that is, it contains more than 
90 degrees, as at B. 



38. K figure, is a surface enclosed by one or more boun- 
daries. 



39. A square is a figure having 
equal sides and four right angles. 



four 




40. A 'parallelogram^ or oblong, dif- 
fers from a square, in having only the 
opposite sides equal. A diagonal line e Z> 
joins two opposite angles, that is, it crosses 



the figure from one angle to another. 



' Both the square and parallelogratn are quadrilateral ; the term is from two 
Latin words quadra, four, and latus, side. Equilateral figures are those with 
equal sides ; thus the square is equilateral, but the parallelo^iaraisnot. 



GEOMETRICAL DEFINITIONS. 



25 




41 . K triangle is a figure inclosed by three 
sides, and which has three angles. If it has 
one right angle, (as h, see triangle A), it is 
called a right angled triangle ; if the sides 
are all equal (as in triangle B), it is called 
an equilateral triangle. The three angles 
of every triangle, together, contain 180 
degrees, or are equal to a semicircle ; the 
four angles or corners of a square, being all 
right angles or angles o^ 90 degrees, con- 
tain 360 degrees, or are equal to a circle. 

42. Triangles contain six parts, viz. three sides and three 
angles ; and if any one side be given with any tv\^o angles, 
or any one angle with any two sides, the other three may be 
found by geometrical operations. This particular branch 
of geometry is called trigonometry.* It enables the astron- 
omer to use the earth as a base wherewith he measures the 
magnitude and distances of the sun and planets ; and the 
navigator on the broad ocean, with no other guide than the 
stars, to ascertain his exact position on the earth's surface. 
In determining the heights of mountains and of buildings, 
and in the operations of the surveyor, this science is 
equally necessary. Although it is not expected that the 
student will understand by the brief explanation here given, 
how to perform these operations, it is something to know 
even the name of the science which teaches them, and to 
obtain a partial view of the principles ■ by which they are 
performed. Thus you will not be disposed to reject great 
discoveries because you cannot conceive how they could 
have been made, like the young person who would not be- 
lieve in astronomy because he could not understand how 



* From the Greek trigonon and metreo, signifying to measure triangles. 



Trigonometry. 



26 



natury\.l PHir.osopHr. 



rnen were able to measure the distance from one star to 
another. The annexed diagram shows 
at one view some of the most important 
geometrical lines and figures. A a is 
the diameter pf the circle 0PM: B a 
radius ; C, a cliprd ; B, an arc ; E, a tan- 
gent ; F, a secant ; G, a CQ-tang^ent ; H, 
t!)e sin,e of the arc ab ; I, the co-sine ; 
l\, the versed sine; L, the sine of the 
arc h O. The sine of an arc or angle 
is the perpendicular drawn from the ex- 
tremity of an arc to the diameter of a circle, as H ; 1 is 
called the co-sine, and K the versed sine; L is the sine of 
complemental arc h C. 




A 



*/ 



LECTURE III. 

OF THE PROPERTIES OF MATTER. 

43. The two essential properties of matter, without which 
we cannot even imagine its existence, are extension and im- 
penetrability. All matter of which we have any knowledge, 
exists in masses called bodies. 

44. All material substances have extension in length, 
breadth and thickness ; these constitute the dimensions of a 
body. Even the air which encompasses the globe is a 
body, and has its dimensions ; — a river has its length, 
breadth, and depth.. The terms height, depth and thickness, 
mean the same thing, although we apply them differently. 
When we measure from the base upward, we call this di- 
mension height, thus we say the height of a mountain ; 
when we measure from the surface downward, we say 
depth, as of a river ; — thickness is not applied to water or 
gasses ; but to solids only, as the thickness of ice, of a 
stratum of rock, &;c. Width is also synonymous with 
breadth. 



Two essential 'properties of malier. Extension. Dimensions. Height, 
depth, ^c. 



OP THE PROPERTIES OF MATTER. 27 

45. The extension of a body, or that space which it oc- 
cupies, is called its volume, and the quantity of matter which it 
contains, its mass. A portion of space which is destitute of 
matter, is called a vacuum. The limits of extension are 
called figure or shape. The productions of nature are sel- 
dom bounded by straight lines ; thus animals and vegetables 
exhibit beautiful curves and a graceful irregularity. The 
rocks and mountains have no determinate forms, and the 
masses which compose them are equally irregular ; but 
crystals present regular geometrical figures, each mineral 
substance appearing to possess its own peculiar form of crys- 
tal as much as each species of plant has its own form of 
leaf. 

46. ImpenetraUIlty is that property of matter by which 
two bodies cannot at the same time occwpy the same space ; 
otherwise any space might contain an indefinite quantity of 
matter ; and bodies instead of resisting, would pass through 
each other, which is contrary to our daily experience. 

47. But air and v/ater are bodies ; you believe you can 
pass your hand through them. Indeed this is a mistake, 
you can no more penetrate the particles which compose 
these substances than those of a board or a piece of metal. 

48. When you move your hand through the air, you do 
not penetrate its particles, but they make way on each side. 
If you plunge your hand into a vessel filled with water, a 
quantity equal in bulk to your hand will flow out. The par- 
ticles which compose air and water move freely, and are 
therefore easily separated from one another. 

49. In solid substances, such as wood and metals, the par- 
ticles are less easily separated ; but a nail may be driven 
into the one, and a rivet drilled through the other ; and in 
coiTimon language vv'e say that they are j)enetrated by the 
nail or rivet ; in these cases, however, as in that of water or 
air, there is a displacing of the particles, for when a nail is 
buried in wood, you can perceive that the fibres of the latter 
substances are crowded more closely, in order to make way 
for the passage of the nail. 

50. You will now understand that by impenetrability is 
raeantjthat any portion of matter excludes from the place which 



Volunic, mnss, figure. Impenetrabilily. Particles of air and tcater no 
penetruLle. A nail does not penetrate the pjrticles. 



2i NATURAL PHILOSOPHT. 

it occupies every other ; and as soon as a body enters into 
any place, it is necessary that the one which occupied it be« 
fore should leave it. This property in bodies may be con- 
sidered as the main-spring of all mechanical science. It is: 
impenetrability which gives the force necessary to motiony 
affording to the oars of boats, to the wheels of mills, and 
various kinds of machinery, and the sails of vessels, a re- 
sistance in the water and air, without which, human inven- 
tion would be unavailing. 

Properties of Matter not considered Essential, 

51. Bivisihillty was long classed among the essential proper- 
ties of matter, but in the present state of science, we cannot 
consider it as such. By divisibility is meant, that we can 
never divide a substance into parts so minute, that it may 
not be again divided ; thus it has been asserted, that matter 
is infinitely divisible. In proof of this opiiiion, it is said that 
any particle of matter must have an upper and under side ; 
every whole must have two halves, four quarters, &;c.* 
The extreme minuteness of division of which some sub- 
stances are capable is considered as a proof of this infinite 
divisibility of matter. We know that a single odoriferous 
flower will perfume a large apartment ; the odour which 
passes from, and comes in contact with our organs of 
smell, is, in fact, particles of the flower itself; but though 
the flower may continue for many days to spread its per- 
fume, its substance does not seem at all lessened by the loss 
of these particles. A small bottle of the otto of rose, or 
other powerful perfume, laid in a drawer, will for years 
continue to impart its odour to the articles near it, and yet 
without any apparent diminution of its substance. The 
small dust obtained by pounding a crystal, when examined 
with a microscope, presents the same form and angles which 
distinguish the mass ; we must then suppose this dust capa- 

' Although it may be impossible, by means of mechanical subdivision, as 
pounding, grinding, &c. to arrive at the ultimate atoms of bodies, yet chemical 
decomposition can effect what mechanical means cannot. 



Two bodies cannot occupy the same space. Divisibility. Exp»mples of ex* 
treme divisibility of matter. 



OP THE PROPERTIES OP MATTER. 



29 



blj of farther subdivision, with instruments sufficiently deli- 
cate. 

52. The microscope reveals to us the most wonderful 
facts with respect to the minute divisibility of matter ; it 
shows us in the fine powder upon the outside of a fig, or the 
rind of a cheese, living beings called cmimalcuIcE, which, 
though so small that many thousands might stand upon the 
point of a fine needle, yet appear in size like droves of large 
animals ; each has its limbs, and the various organs which 
are necessary to carry on the functions of animal life. While 
the filaments of a spider's web appear like the largest cable, 
being formed by the union of a multitude of smaller cords. 
Suppose that some one should construct an instrument 
(and the supposition is not absurd,) which, in its magnifying 
powers, should exceed any microscope now known, as much 
as that does the unassisted powers of the eye ; what new 
wonders would be revealed to us, and what new proofs of 
the wonderful divisibility of matter. But examples showing 
that matter is divisible to a wonderful extent, do not abso- 
lutely prove that there may not be ultimate or last particles 
which cannot be divided. 

53. Geometry teaches 
that space is infinitely divi- 
sible ; in this science it is 
taken for granted, that a 
line, however small, may 
be divided. It may be de- 
monstrated that the line a i, 
Fig. 1, is capable of being 
divided into any number of 
equal parts. Draw a line 
A I, parallel to a i, of any 
length, and at any distance 
you please, and divide it 
into as many equal parts. 
A B, B C, C D, D E, &c. 
as the small line given, is 
to have divisions, say eight. 

Now draw throuo'h the ex- 




Discoveries by means of the microscope, 
infinitely divisible. 

3* 



Bpace proved b}' geouie tiy ro 



30 NATURAL PHILOSOPHY. 

tremities A a, and I i, the straight line KaO,l i O, till they 
meet in the point O ; and from O draw towards the points 
of division B, C, D, E, &c. the straight lines O B, C, O D, 
O E, &;c. which shall likewise divide the smaller line into 
eight equal parts. This operation, mathematically speak- 
ing, may be performed, however small the given hne a i, 
and however great the number of parts into which you pro- 
pose to divide it ; though in executing geometrical figures, 
the lines may touch each other and lose their distinctness, as 
may be seen near the point O, because lines which we draw 
have some breadth. Thus, physically, this proposition is 
not true, though, mathematically speaking, there is no Hne, 
however small, but may be again divided. 

54. But space is not matter, therefore if its infinite divisi- 
bility were demonstrated, this would not prove the infinite 
divisibility of matter. Philosophy leaves this subject unde- 
termined, but chemistry, a sister science, comes to our aid, 
and informs us that by the analysis of bodies, she has dis- 
covered that they are composed of atoms f or particles which 
cannot he again divided.^ These ultimate atoms are termed 
by many writers molecules '\. 

55. In a piece of sponge, or light bread, you perceive 
pores or interstices, these are filled with air ; put the sponge 
or bread in water, and the air will escape in little bubbles, 
and give place to the water. The pores in wood and metal 
are less visible, but yet they exist. Every house-keeper 
knows that oil spilled upon her oaken or pine floor is absorb- 
ed by the pores in the wood, and is only removed by the 
application of such substances as soap or lye, which, by 
uniting with the oil, change its nature, and thus destroy its 

* The word atoms is from the Greek, and signifies that Avhich cannot be 
lurther cut or divided. 

t Although in late works on Natural Philosoph}-, divisibility has been in- 
sisted on as an essential property of matter, the doctrine of atoms or indivisible 
particles is by no means modern. Sir Isaac Newton says, " all things con- 
sidered, it seems probable that God in the beginning, fovu;ed matter in solid, 
massy, hard, impenetrable, moveable particles of such sizes and figures, and 
with such other properties, and in such proportion to space, as most conduced to 
the end for which he formed them. 

X A term from the Greek which signifies little masses. 

Chemistry proves the existence of ultimate atoms. Porosity. Examples o 
porosity. 



OP THE PROPERTIES OP MATTER. 31 

effects. Metals formed into thin globes and filled with a 
liquid, on being subjected to powerful pressure, have ex- 
hibited their outer surface covered with the moisture exuded 
through the pores. The diamond, the hardest of all known 
substances, admits the passage of light ; and as matter is 
impenetrable, we must consider this, and all other cases of 
transparency, as owing to the porosity of the substance. 

56. Density is in an inverse proportion to porosity ; that 
is, the more porous a body is, the less is its density. Sponge 
is less dense than wood, and wood is less dense than iron. 
The metals vary in their degrees of density ; platina is 
more dense than gold, and gold is more dense than silver. 

57. Owing to the porosity of matter, all known substances 
are more or less compressible ; that is, capable of being 
made to occupy less space by means of forcing the particles 
which compose them into closer contiguity. You can press 
a sponge, or a lock of wool, by the muscular force of your 
hand, because these bodies being very porous are easily 
compressed. The more dense a substance is, the less it is 
compressible. Hardness and softness are terms which, in 
common language, signify the same properties as density 
and Compressibility. 

58. Expansion is that property of matter whereby the 
particles which compose a body are divided to a great dis- 
tance, and thus occupy more space than in their ordinary 
state. Divisibility, porosity, density, compressibility and ex- 
pansion, though common to all matter of which we have any 
knowledge, are not ranked among its essential properties, 
because we can imagine that matter might exist without 
them, while we can form no notion of matter that is not 
extended, and does not occupy space, so that where that 
is, another body cannot be ; or in other words, we con- 
sider extension and impenetrability as the only essential 
properties of matter. 

Inertia. 

59. Matter is inactive ; it has neither the power to move 
nor to stop its motion ; this property is called inertia, a 

Density. Compressibility. Expansion. Divisibility, porosity, &c. not 
essential properties. Definition. 



32 ' NATURAL PHILOSOPHY. 

term which was introduced into philosophy by those who 
maintained that all bodies have a propensity to rest. They 
considered matter as somewhat resembling indolent persons, 
who prefer rest to exertion, and ascribed to bodies an aver- 
sion to motion, similar to that which sluggards have for 
labour ; the term inertia signifying nearly the same thing 
as sluggishness. This opinion was founded on a false view 
of the nature of matter, vv^hichis incapable of desire or aver- 
sion, and therefore neither likes nor dislikes rest or motion. 
It requires as much force to put it into one state as the 
other. 

60. We know that m.atter never begins to move itself, 
that a stone, for example, never raises itself from the ground, 
or moves in any direction. A stone thrown from the hand, 
after moving for a time, at length falls to the earth, and its 
motion ceases. You may ask, does not this prove that the 
stone has a tendency to rest rather than motion. We an- 
swer, that force is equally necessary in the one case as in 
the other, although the exertion of it is not equally apparent 
in both cases. You see the force used by the hand to throw 
the stone, but cannot see that which stops it. 

61. The resistance of air impedes the motion of bodies; 
and besides this, there is constantly in operation a powerful 
force, called the attraction of gravitation, which tends to 
bring to the earth all substances within its sphere of action. 

A top whirled from the hand, spins swiftly at first, but 
gradually moves more slowly, until its motion ceases, and it 
rests upon the floor. The fiiction, or rubbing against the 
floor, the resistance of the air, and the attraction of gravita- 
tion, are the united forces which stop the motion of the top, 
or by their continued operation, at length overcome the im- 
pulse at first given by the force of the hand. Inertia, then, 
is that property of matter by which it resists any change of 
state, whether of rest or motion. The inertia of a body is 
proportional to its quantity of matter, or which is the same 
thing, to its weight. 

Opioiou of ancient philosopliers. Force as necessary to stop motion, as to 
produce it. Forces which put a stop to motion. 



OP THE PROPERTIES OP MATTER. 33^ 

Attraction and Rqmlsion. 

62. There are in nature two opposite powers, attraction 
and repulsion, the former tends to bring the particles of 
matter together, the latter to draw them asunder. These 
powers, by the Creator and Governor of the universe, are 
made to balance each other ; were it otherwise, disorder and 
ruin would prevail in the material world. 

63. Should attraction reign uncontrolled, the particles 
which compose bodies would rush into such close contact, 
that, according to the opinion of some philosophers, our 
globe and all that it contains might be compressed to the size 
of an apple. We know that nearly two thousand gallons of 
steam may be condensed to one gallon of water. 

64. Repulsion operating without any check would destroy 
the solidity of all bodies on the earth, and even the earth it- 
self, which would exist only in the form of the most rarefied 
gas. The burning of a log of wood shews us a solid body 
passing off in vapour, since ail that remains solid is a small 
quantity of ashes which bears but a very small proportion to 
the size of the whole log. The great agent in repulsion is 
the principle of heat called caloric, the consideration of whicli 
Belongs to Chemistry. 

Cohesive Attraction, 

65. Attraction is of different kinds ; we shall first notice 
that of Coliesion. This takes place between bodies which 
are in contact. The table, the iron stove and looking glass 
are composed of very small particles of matter held together 
by the power of cohesion, without which they would fall in 
pieces and form a heap of loose particles with as little unity 
as so much sand. When you attempt to separate the par- 
ticles of a solid body you perceive that they are held togeth- 
er by a power which requires more or less resistance to 
overcome. This is called cohesive and sometimes adhesive 
attraction, and may be exemplified by many simple experi- 
ments. If two leaden bullets are scraped very smooth, and 
pressed together, they will seem to be held in contact by a 
force which requires some effort to overcome. Two plates 

Opposite powers. Uncontrolled attraction. Uncontrolled repulsion. Ef- 
fect of Cohesion. Experiment. 



34 NATURAL PHILOSOPHY. 

of glass when placed together will cohere so strongly as not 
to be easily separated. 

66. Liquids are less influenced by cohesive attraction than 
solids, but in drops of devv' suspended from the leaves of plants, 
we see the operation of this power both in the globular form 
which the particles of moisture assume, and in their remain- 
ing attached to the leaf when the natural tendency v/ould be 
to fall off. Mercury or quicksilver is a metal existing in a 
fluid state. If small globules of this metal are placed upon 
a plate of glass or other smooth substance, they will be seen 
to move towards each other and unite. In order that this 
should take place, the globules of mercury must be brought 
within the sphere of their mutual attraction. Liquids in com- 
mon language are said to be thick or thin according as the 
cohesive attraction is more or less powerful, but dense and 
rare are terms more scientific ; thus quicksilver is said 
to be a dense, and air a rare fluid. 

67. It is by the attraction of cohesion that liquids arrange 
themselves around a common centre in globular forms; thus 
Aew, which is moisture existing in the atmosphere in very 
minute particles, may be seen in the morning suspended in 
drops from the leaves of plants, and adhering to the blades of 
grass. 

Capillary Attraction, 

68. Capillary* attraction is that power by which liquids 
rise through minute tubes. This is probably only a form of 
cohesive attraction. The fluid appears to creep along as if 

Fig. 2, attracted by the contiguous particles of the tube. 
The figure represents a glass partly filled with 
water and having a small tube placed within it; 
the fluid in the latter is seen at A above the level 
at B. It is also seen that the fluid at B is con- 
cave, or higher at the sides than the middle ; 
this is in consequence of the attraction of the 
particles of matter which compose the ring of 
the glass contiguous to the upper surface of the 
fluid. 

* The term ca*]lary, is from the Latin capilln?, a liair. 

Cohesion in liqiads. Globular foini of liquids. Experiment to illustrate 
capillary attraction. 




OF THE PROPERTIES OP MATTER. 35 



fi^. 3. 




69. The larger the hore of the tube the less is 
the attractive power. If two tubes of different 
diameter be immersed in a vessel of coloured wa- 
I ter, it will be found that the liquid will rise as 
mucii higher in the smaller tube B, as the diame- 
ter of its base is less than that of the larger 
tube C. 

70. The power of capillar}' attraction is manifested in a 
variety of common occurrences; if one end of a piece of 
bread be dipped into water, the liquid will soon make its way 
until the whole is moistened ; the same thing may be seen in 
a spono^e, and one wlio carelessly lets an end of his towel fall 
in the basin of water, in the m .-niing finds the v/hole towel 
vv^et. In New England, where the females are celebrated for 
industry, especially in the department of knitting, it is not 
uncommon to see many pairs of cotton stockings of domestic 
manufacture, spread upon the grass to bleach, with the toes 
lying in a flat vessel containing soap suds. Now it is this 
power of capillary attraction which carries the suds through 
the minute pores of the cotton, and keeps the whole fabric in 
a state of moisture favourable for the bleaching process. The 
wicks of candles and lamps supply the flame by means of tal 
low or oil, which ascends through the capillary tubes of the 
cotton. 

71. You might ask if the mercury of the thermometer does 
not rise by means of the attraction of the sides of the glass 
tube which contains it ; it does not, because in order that ca- 
pil/ary attraction should take 'place, the tube must he composed 
of a substance which attracts the particles of the liquid with- 
greater force than they attract themselves. The particles of 
mercury cannot be attracted by those of glass ; but in small 
tubes of tin or silver, mercury rises, and also in glass tubes 
coated with oil. 

72. From the explanation now given, you will perceive 
that capillary attraction is only another form of cohesion ; 
in modern science both are included under the general term 
molecular attraction. By molecules is understood very minute 

Second experiment. Examples of capillary attraction. What is nocossary in 
ordov tliat this mode of attraction may take place Ptloleciilar attraction. 



3Q NATURAL PHILOSOPHY. 

particles or atoms of matter. They are those which cannot 
be divided, and are therefore called ultimate or last atoms. 

73. Chemistry teaches that all the matter upon the globe 
is composed of about fifty elements, or bodies which consist 
of the same kinds of molecules. Water is not an elementary 
body because it can be decomposed into two kinds of 
molecules. These are the gasses, 0x5 gen and hydrogen, 
but neither of the latter are capable of decomposition, there- 
fore they are called elements. 

74. When the body is elementar}^, as a piece of sulphur, 
it is said to consist o^ integrant molecules. When it is a 
com.pound body as water, which consists o^ one molecule or 
atom of oxygen united to two of hydrogen, these are called 
constituent molecules. 

75. Cohesion and capillary attraction, then, are the attrac- 
tion of molecules ; the first operates when the molecules of a 
body are attracted towards each other ; the second operates 
when the molecules of a liquid are attracted by those of bo- 
dies adjacent to them. 

76. Chemicdl attraction or affinity is that force which 
unites the elements of bodies to form compounds, as hydro- 
gen and oxygen to form water, and unites the molecules of 
compound bodies to form new and different compounds, as 
oil, lye, and water, which combined, form soap. Chemical 
attraction cannot, like that of cohesion, be overcome by means 
of pounding, grinding or cutting. Marble is a compound of 
lime and carbonic acid, chemically united. Let a piece of 
this stone be ground to powder, ever}' particle of the dust 
will still be compounded of its constituent atoms or molecules ; 
b}^ heating the marble, however, the carbonic acid may be 
•driven out and the force of chemical attraction overcome. 

77. Magnetic attraction is the power which a certain iron 
ore called the loadstone or magnetic iron, has of drawing to- 
wards it portions of iron or steel ; it has also the power of 
com.mimicating to iron and steel its peculiar properties. Thus 
a knife y/hich has been rubbed upon a magnet, if held near a 
needle, will cause it to mov-e towards it, or if presented to 
iron filings will produce the same effect. When a piece of 
magnetic iron or an artificial magnet is placed upon a point 

Molecules of water. Integrani molecules. Cohesion and capillary aftraction 
included under molecular attraction. Cbemical attraction. Maornetic attraction. 



GRAVITY. 37 

or suspended by a string, its ends will always point towards 
the north and south, thus it is said to have a north and soutli 
pole. 

78. ^Electrical attraction is a propertj^ which certain bo- 
dies possess, when ezcited by rubbing, of attracting other 
bodies, and frequently of throwing out sparks or streams of 
light. If a sheet of paper be rubbed briskly with a stick of 
sealing wax, its edges will be alternately attracted and re- 
pelled when held towards the wax. A glass cylinder rubbed 
with a piece of silk will alternately attract and repel light 
substances. The fur of a^ cat when rubbed, throws off bril- 
liant sparks accompanied with a crackling noise. The term 
Electricity is from the Greek electron, amber, because the 
electric fluid was first discovered in this substance. The 
subjects of Magnetism and Electricity, will hereafter be more 
fully considered. 



LECTURE IV, 

GRAVITY. 



79. All terrestrial bodies fall toward the earth when they are 
not supported. Before the 17th century, mankind had never 
thought of inquiring why bodies thus fell. It is related that 
the fall of an apple from a tree under which the then young 
Sir Isaac Newton was sitting, was the ocasion which led him 
to philosophize on the subject of falling bodies. Why, he 
thought, did this apple take a downward, rather than an up- 
ward direction, or why did it move at all? There can be no 
motion without force ; the tree did not push the apple down, 
where then is the force which caused its descent ? In consid- 
ering the subject farther, he reflected that the earth every 
where attracted bodies towards its surface, in the deep val- 
leys and upon the high mountains. This power of attrac- 
tion he called gravitation. 

Electrical attraction. Discovery of gravitation. 

4 



38 Natural philosophy. 

80. It was somethiDg to have been the first to reflect and 
reason upon the cause of a fact, which had escaped the 
inquiry of all preceding generations. But Newton stopped 
not here, he beheld the moon pursuing her regular course 
around the earth, and was led to inquire whether she was 
attracted towards the earth ; and if so, why she too did not 
fall upon its surface. The result of his inquiries and reason- 
ing, was the discovery that gravitation is not confined to the 
earth, but that its power pervades the solar system, causing 
not only the motion of the moon around the earth, but the 
revolutions of the earth, and other planets around the sun. 
There are reasons, also, for believing that the same principle 
of gravitation operates in the most distant regions of space^ 
binding together other solar systems, and perhaps causing 
them to revolve around some common centre. 

81. The attraction of gravitation^ or gravity^ is that fores 
hy which distant bodies tend towards each other ; it differs 
from cohesion and chemical attraction because it does not 
require the particles of matter to be brought in contact, but 
acts on remote bodies like electricity and magnetism. Al- 
though we have a name to express this force, we know in 
reality nothing of the cause of attraction ; even Newton him- 
self was here no v/iser than the*most ignorant of mankind. 
Some have imagined that a sab(|je, invisible fluid, issues from 
bodies, which is constantly te^:ding to draw them together^ 
But we have nothing to do with speculations unsupported by 
observation, and experience ; our object is to learn some of 
the phenomena* of gravitation, for these the Almighty has 
given his creatures power to understand. 

82. Our vievv's will now be directed to terrestrial gravity, 
or the effect which the earth's gravity has upon bodies near 
it. All bodies tend towards the centre of the earth hy the 
attraction o^ gravitation. This is not owing to any peculiar 
pov/er of attraction in the centre, but because the earth being a 
globe its centre is that point towards which each of its own par- 
ticles is attracted, and thus it becomes the centre of attrac- 

' Phenomenon in common language signifies some extraordinary appearance ; 
in science, it means merely a change or appearance. PTienomenais the plural 
of phenomenon. 

Its extent. Definition of gravity. Cause of gravitation unkno^vn. Tenes- 
trial gravity, 



GRAVITY. 



59 




lion to other bodies. Tiie terms upward and doivnivard have 
relation to what is fiirthest from, or nearest to the surface of 
the earth, every part of vi^hich is equally distant from th j 
centre ; the slight inequality of mountains and valleys, belr.g, 
in comparison with the whole circumference, of no percepti. 
ble importance. Let the figure /ep- 
resent the globe of the earth ; now 
suppose bodies could fall freely from 
any point on its surface throu^i^h its 
diameter ; a ball dropped from ei- 
^ther of the points, A B C D Jj: F 
G H I would be attracted tov/ards 
O at the centre, and move in a 
straight line to that point \r here it 
would rest. The lines a A, b B, c C, 
d D, &c., are all vertical and point 
downwards or to the centre ; thus you perceive that, all bodies 
will fall perpendicularly to the surface of the earth, and if not 
impeded would penetrate to the centre. By joining the lines 
without the circle to the centre at 0, you may better under- 
stand this. 

^^ 83. The real figure of the earth was 

not understood by the ancients They 
supposed it to be a fiat mass of matter 
as represented in the figure, whose sur- 
A B face only was habitable, and that A B 

were the extreme impassable points. When the opinion was 
first advanced that the earth was a sphere, and that there 
were inhabitants on opposite sides of its surface, it was con- 
sidered as a wicked and abominable heresy, and treated v/ith 
great severity, both by civil and ecclesiastical rulers. "If there 
are people," said they, " who live on the under side of the 
globe, they must have their heads downwards and their feet 
upwards ; and how could they hold fast to the under side of 
this ball ? It is an insult to religion and common sense to 
pretend such a thing.'^ Some attempted to explain the mat- 
ter by asserting that their antipodes* held to the surface of 




* Antipodes is from the Greek anti against, and pacles I'cct. 



Opinion of die ancients respecting the form ol'tlie earth. 



40 



NATURAL PHILOSOPHY. 



the earth as insects crawl on the under as well as the upper- 
side of a small globe. But they did not reflect that the insect 
.adheres thus by means of its claws. But navigators insail- 
in'g around the globe have neither found people with clawsy 
no J any who considered themselves as living on the un- 
der side of the globe ; all alike have the broad arch of the 
hea\^ns above, and the firm earth beneath them. Besides, 
let us recollect th-at in twelve hours, 
by the earth's rotation on its axis, we 
shall be exactly in that part of the 
sphere where our antipodes now are. 
The figure represents the sphere of 
the earth and two figures standing at 
opposite points ; let each at the same 
time drop an apple, both apples would 
fall towards the earth, and supposing 
they were able to pass freely through- 
it, they would penetrate to the centre 
and unite ; here they would rest and 
not fall either way, being attracted 
equally on all sides. 

84. Have you ever thought what made bodies heavy, or, 
which is the same thing, what caused their weight ? It is the 

force with which they are attracted to the earth, and this force 
is in proportion to their quantity of matter. This quantity of 
matter does not depend on the size of the body ; a piece of 
lead weighs much heavier than a block of wood of the same 
size, because the lead has m.ore density than the wood ; that 
is, within the same bulk it contains more particles of matter. 

85. As the force of the earth's attraction is in proportion 
to the quantity of matter, you will perceive that if this were- 
doubled, bodies near its surface would weigh as much againj 
as they now do, or if the earth contained only half its present 
quantity of matter, the weight of bodies would be lessened 
in the same proportion. 




Cause of weight. In what case bodies would weigh double what they now doi. 




GRAVITY. 41 

86. Weight is measured by means of steel- 
yards, or a balance ; in the latter, pieces of 
lead or iron, as ounce and pound weights, are 

I J taken as measures. In the balance, are two 
scales, which, when empty, are exactly in equi- 
poise. A merchant wishing to weigh a pound 
of tea, puts into the scale a, a pound weight, 
which by its gravity causes the §cale to de- 
scend ; as the tea is put into the other scale b, 
a begins to rise, and when the mass of tea 
equals that of the leaden pound weight, the two 
scales are again in equipoise. 

87. There is a great difference in the bulk 
of the leaden pound weight and that of the pound of tea, thus 
we say the specific gravity of the one is less than that of the 
other, meaning that a given bulk of tea does not contain 
an equal quantity of matter as the same bulk of lead. 

88. We have said that all terrestrial bodies are attracted to 
the earth ; you may ask whether this be the fact with respect 
to smoke, steam, and other vapour, and especially the gas* 
used to inflate balloons, which not only raises the balloon but 
carries persons with it into the higher regions of tli^e atmos- 
phere. If you plunge a block of wood into a vessel of water 
you will see it rise and float upon the surface; this is because 
-the specific gravity of wood is less than that of water, the 
heaviest body being most strongly attracted, forces the lighter 
one above it. Lumps of iron or lead, which are specifically 
lighter than quicksilver, on being thrown into a vessel con- 
taining the latter metal vvill swim on the surface, and if 
forced down will re-ascend ; but gold or platina in the same 
situation will sink, because their specific gravity is greater 
than that of quicksilver.' 

89. Air being lighter than the solid and liquid bodies on 
the earth, keeps its place above them ; but yet the air has 
weight, or is subjected to the universal law of gravitation. 
The air near the surface of the earth is more dense than in' 

" H3'drogen. 

Measures of weight. Specific gravity. Vi'hy some bmlies i ise niid uthors; 
sink, 

4* 



42 NATURAL PHILOSOPHY. 

the upper regions. Persons who ascend high mountains, or 
rise to great heights in balloons, find a difficulty in breathing 
on account of the rarity of the air. You can readily under- 
stand that the increased density in the lower parts of the 
atmosphere is owing to the pressure of the upper portions ; 
this has been well compared to that pressure which takes 
place with respect to the lower fleeces in a pile of wool; 
which are thus more compact or dense. 

90. Pressure, as well as the motion of falling bodies, 
proves that attraction is universal ; when you hold a stone in 
your hand, you feel this pressure in proportion to its size ; you 
are sensible that a force is in operation tending to draw the 
stone downwards. 

91. As the force of gravitation is proportioned to the quan- 
tity of matter, it follows that all bodies fall with equal velo- 
city, if they meet with no resistance. A feather and a leaden 
bullet dropped from a window together, would reach the 
ground at the same instant, were it not for the resistance of 
the air, which the lighter body does not so easily overcome. 
If you drop a pebble into a tub of water, and another into a 
tub containing only air, you will observe that the pebble in 
the latter soonest reaches the bottom. Now if you had a 
third tub which was really empty or exhausted of air, you 
would perceive, on making the experiments, that a pebble 
would fall through the same space in this, in still less time 
than through the air. Here then you see that the medium 
through which bodies fall impedes their descent, and this, 
in an inverse* proportion to their specific gravity. By means 
of an apparatus called an air-pump, which will be described 
hereafter, we are able to exhaust or pump out the air from 
vessels, placed over it. 



* By inverse is meant contrary to, or the opposite of, from the latin in and ver- 
to to turn bacli or 



Air of unequal density. Cause of pressure. Why all bodies do not fall 
with equal velocity. 



GRAVITY. 



43 




92, The figure represents at A, a tall 
bell glass, having at the top a brass cover 
B, through which passes the wire C, sap- 
porting a small stage, the two sides of which, 
D D, incline downwards when the wire is 
turned. Suppose upon this stage are put a 
piece of lead, E, and a feather, F, the air 
then being exhausted from the bell glass 
by being placed over the plate of an air- 
pump G, the wire is turned, and the lead 
and the feather being deprived of support 
by the inclination of the stages D D, both 
strike the plate G at the same moment. 

93. All bodies equally gravitate towards the earth. Every 
particle of matter on its surface and within its atmosphere is 
attracted towards the earth, and whether the number of these 
particles be 500 or 1000, the earth's power of attraction will 
be in proportion. If you take in one hand an ounce, and in 
the other a pound, weight, you can raise them both at the 
same instant ; but for the larger weight you exert more 
power. You may indeed find bodies too large for you to 
move. The earth C3.nnot perceptibly draw the sun out of its 
place, though it powerfully affects the moon, and conquers 
by its attractive power all terrestrial objects which are not 
supported by cohesion or some counteracting force. 

94. The resistance of the air is always in proportion to the 
surface of bodies ; a lump of gold that would, in falling, seem 
little impeded by this resistance, may be hammered into thin 
sheets called gold leaf, so that the same particles of matter 
shall cover a surface many millions of times greater, and the 
increased resistance of the air will be in proportion to the 
increase of surface. 



Experiment to shew the resistance of the air. Attraction of gravitation pro- 
portioned to the gravitating particles. Resistance of the air in proportion to the 
surface. 



44 



NATURAL PHILOSOPHY. 




05. Bodies in falling, unless drawn by some 
other force, always move in the direction 
we call downward, or in lines perpendicular to 
the surface of the earth ; this line is also called 
vertical. If a small bit of lead be suspended by a 
cord, that cord will be stretched out in a straight 
line, and that line will be vertical. Such a line 
is called by mechanicks a plumh line, the name 
being derived from the Latin, plumbum, lead ; 
sometimes it is called a plummet line. Masons 
erect the walls of buildings by such a line. 
The floors of a house should be in a horizontal 
plane or level, to which the walls and partitions 
are perpendicular. 
96. A plummet line suspended from a high mountain is 
drawn out of its perpendicular towards the side of the moun- 
tain ; this is owing to the attraction of the mountain, which 
though so small in comparison to the whole earth is capable 
of interfering with the earth's attraction, because its distance 
is less from the attracted body. 

97. No two bodies can fall to 
the earth in parallel lines, for 
as they are all attracted to the 
centre, the lines if produced 
must continue to approach until 
they meet in that point. Thus 
the two sides of a pair of scales 
do not hang exactly parallel to 
each other, as may be seen in 
the figure ; A B C represents the 
earth's sphere, E D a balance 
suspended over it. The lines 
D F and E F which meet in the 
centre of the sphere are not 
parallel, for parallel lines if pro- 
duced to any length never meet. 
The convergence* in common 
scales is too light to be percepti- 
ble to our senses ; but in the fig- 

Converging lines are such as incline toward each other, and if sufficiently cx" 




mded would at length meet 



Vertical line. Plumb line drawn 
the earth in parallel lines. 



by attraction. Bodies do not fall to 



GRAVITY. 45 

ure the beam of the scales is represented as extending through' 
several degrees. 

98. Where there is no attraction of gravitation there can 
he no weight. If there were but one body in the uni- 
verse it is evident that this would be attracted by nothing ; 
of course it would remain at rest ; and, though it were 
of the magnitude of the sun together with all the planets, 
it would not press in any direction sufficiently to counter- 
balance the weight of a feather. 

99. The force of gravitij is greater at the surface of the 
earth, from whence it decreases both upivard and downwards 

In ascending from the surface of the earth, the force of gravi- ' 

ty decreases as the square of the distance from the centre. tfyf^CA 

100. By the square of any number, we mean that number 
multiplied by itself; thus the square of 2 is 4, the square of 
4 js 16, the square of 16 is 256, and the square of the last 
number would be that number multiplied by itself, and soon. 
A body which at the surface of the earth, viz : 4000 miles 
from the centre, would weigh one pound, or sixteen ounces, 
if carried to twice this height from the centre, namely, 8000 
miles, would weigh ^ of a pound, or four ounces ; if carried 
4000 miles higher than this, which would be three times the 
distance from the centre, its weight would be diminished to 
■i- of a pound, or less than two ounces. The moon is about 
60 times as far from the centre of the earth, as the distance 
from that centre to the surface, therefore^as the square of 60 
is 3600,* the attradfijon of the earth ^»Si the moon is 3600 
times less than i^>@n the earth's surface ; so that a body 
which here weighs one pound, would at the distance of the 
moon, weigh only the three thousand and six hundredth part 
of a pound. 

101. The force of gravity from the earth^s surface down- 
wards, decreases simply as the distance, so that at 2000 miles, 
or half way from the surface to the centre, a body weighing 

* The square of sixty is this number multiphed by itself, thus : 60 

60 

3600 

In what case would there be no altraction % Where is gravity most powor- 
ful? The square of any number. Change in weiglit abe^^e the surface of tlie 
Earth. Change in weight below the surface of the Earth. 



m NATURAL PHILOSOPHY. 

a pound at the surface would weigh but half a pound at 3000 
miles, or three fourths the distance from the surface to the 
centre, it would weigh but one quarter of a pound, and at the 
centre it would have no weight. 

We must now turn our attention to ether subjects, but 
shall have frequent occasion to refer to gravitation as con- 
nected with the most important physical phenomena. 



LECTURE V. 

MOTION. 

102. All bodies are either in a state of rest or motion. 
They have no tendency to the one state more than to the other. 
When a body is once in a state of rest, it will always con- 
tinue so, if nothing external act upon it ; and if it begin to 
move, we know the cause of motion must be external, for 
there is no power in matter to put itself in motion. 

103. Existence, and all that renders it valuable, is the 
result of motion. A person reclining on a sofa, would per- 
haps think he spoke correctly in saying, " my body is now 
in a state of rest," but a very little philosophy would teach 
him that so far from this, the most complicated machinery 
was in constant operation vvithin his own frame. The lungs 
alternately inflating themselves with air and throwing it off, 
as in the blowing of a bellows ; the stomach also, is at 
work in digesting the food, and taking the first step towards 
converting it into blood, to supply that great reservoir the 
heart, which sends forth its rushing currents into every part 
of the system ; one portion passing off in the form of insensi- 
ble perspiration through the pores of the skin, and another 
portion, forming new flesh, to restore the daily waste of 
nature. 

104. The plant, too, which seems fixed and motionless, is 
within itself in ceaseless activity, the root labours to take in 

Have bodies a greater tendency to rest than to motion?- Continuation of life 
the result of molion. Motion going on within plants. 



MOTION. 47 

from the surrounding soil, the stores which the trunk and 
branches need for their support, the leaves are busied in se- 
lecting from the air, and the gasses floating in it, the materi- 
als which are needed for the firmness and strength of the 
plant, and in decomposing and throwing back into the air 
what is superfluous.* But these internal motions among the 
particles of living beings, belong to another science than the 
one we are considering. f 

105. But here is a stone lying upon the ground, there is 
no action of vessels within this mass of matter, therefore you 
will say, the stone surely is at rest. But no, the stone is 
not absolutely at rest, since by the earth's diurnal motion, it 
is whirled with great velocity, and is also moving rapidly by 
the earth's yearly circuit around the sun. But as respects 
all the objects on the earth, the stone is at rest. In treating 
of the subject of motion, we are to consider it only in relation 
to the changes of terrestrial bodies with respect to each oth- 
er ; in this view, motion may be defined a change of place. 

106. Absolute motion is a change of place, with respect 
to any fixed poiut, as a person walking or riding is in abso^ 
lute motion. 

107. Relative motion, is a change of place in a body in 
motion with respect to another body also in motion. Sup= 
pose a person standing on that part of the deck of a steam= 
boat farthest from the shore, should, at the moment of the 
boat's starting off, begin to run towards the shore, and move 
at the same rate of the boat to the other end of tlie deck ; iiis 
position with respect to the objects on shore would be exact- 
ly what it was when the boat started, though changed in re- 
lation to the boat. 

108. Apparent jnotion, is owing to the real motion of the 
spectator. Every one who has sailed upon a river bordered 
v/ith villages and populous towns, has observed how rapidly 
they seemed to move backwards, as the -boat glided along ; 
but reason here contradicts the evidence of the senses, for, 
notwithstanding appearances, we are certain that it is our- 
selves, and not the towns, that are in motion. 

' Carbonic acid is the gas retained, oxygen tljat which is thrown iff. 
t Physiology. 

Definition of motion. Absohite motion. Relative motion. Apparent aiotion. 



48 NATURAL PHILOSOPHY. 

109. The motion of the earth on its axis causes the ajma- 
rent motion of the sun, thus we say "the sun rises or the 
sun sets," as the passenger on board a vessel says, "the 
shore is receding from us." 

110. We have remarked upon a property of matter call- 
ed inertia, or a passiveness with regard either to motion or 
rest ; therefore, as tliere is nothing within, which can put a 
body in motion, this effect is produced by the agency of some 
external power, and this is called/bree. 

111. Force may be muscular, as in the action of men and 
animals, or mechanical, as in the action of wind, water, steam, 
and gravity. 

112. Velocity is a term applied to bodies in motion. 
When we see a bird darting through the air, we say it moves 
with great velocity ; a tortoise moves with' little velocity ; 
that is, the time in which the bird and the tortoise would 
pass over a given space would be very different. 

il3. The velocity of motion, then, is estimated by the 
time spent in moving over a certain space, or by the space 
moved over in a certain time. The less the time, and the 
greater the space moved over, the greater is the velocity ; 
but the greater the time, and the less the space moved over, 
the less is the velocity. 

114. 1st. To ascertain the degree of velocity, divide the 
space by the time ;— thus, suppose a person travels thirty 
miles in 6 hours ; in order to know his velocity divide 30 by 
6, the answer is 5, that is, he travelled at the rate of 5 miles 
an hour, thus velocity equals space divided by time. 

115. 2d. To ascertain the time in which motion is perform- 
ed, divide the space by the velocity ; — thus, if a man has 
travelled 30 miles, at the rate of 5 miles an hour, as 30 di- 
vided by 5 is 6, the last number is the time in which he per- 
formed the journey. 

116. 3d. To ascertain the space moved over, multiply the 
time into the velocity ; — thus, 6 hours representing the time, 
is multiplied by 5, which stands for the velocity, or rate of 
motion, the answer is 30, which stands for space or distance 
travelled. 

117. Thus where any two of the three circumstances, ve- 

Case of the apparent motion of the sun. Force. Of what kinds ? Velocity. 
■How estimated ? Rule 1st. Rule 2d. Rule 3d 



MOTION AND FORCE. 49 

locity? time, and space are given, the third may be ascer- 
tained. The rules above given apply only to cases o^ uni- 
form motion, that is, when the body passes over equal spaces 
in equal portions of time, as the index of a clock. 

118. Accelerated motion, is v^^hen the spaces described in 
equal portions of time continually increase, as we shall find 
to be the case with bodies falling with the force of gravity. 

119. Retarded motion^ is when the spaces described in 
equal portions of time continually decrease, as the motion of 
a body thrown upwards is continually retarded by the earth's 
attraction. 

Motion and Force. 

120. The momentum of a body is its moving force, or its 
quantity of motion, and this is in proportion to its weight and 
velocity. 

A cannon ball thrown against a person, with the hand, 
might have only momentum enough to bruise the flesh, while 
the same ball shot from a cannon, would pass through his 
body . The weight in both cases would be the same, but 
the difference in the velocity would make the difference in 
the momentum. 

121. A block of wood, floating slowly against a person's 
limb, suspended from a dock, would scarcely be felt, while 
a loaded vessel moving at the same rate would crush it. 
Here the velocities are the same, but the weight different. 

122. The bo}?- v/ho throws a ball, or shoots a marble, 
knows that its force, or momentum, is in proportion to its 
velocity ; that the same ball will strike twice as hard if it 
move twice as fast, or ten times as hard if it move ten times 
as fast; now let the word momentum be substituted for hard, 
and velocity for fast, and you have the fact scientifically ex 
pressed. 

123. The momentum of bodies is one of the most impor- 
tant principles in mechanics, because it is by opposing 
matter to motion, that machines derive their powers. 



In whatrasps do these rales apply 1 Accelerated motion. Retarded motion. 
Momentum. Momentum caiised by velocity. Momentum of weight. Terms 
substituted for mom(intuin and velocity. Howdo aiachincs derive their power; 

5 



'v?|s 



HiiiiiiiiiliB 



50 NATURAL PHILOSOPHY. 

Fig- 13. 124. Force, may bs 

defined, that cause which 
moves, or tends to move, 
a body ; or which chan- 
ges, or tends to change, 
B its motion. If the ball 
a be placed gently against the block b, the force will not be 
sufficient to move it ; but let the same ball be placed at c, 
and rolled down the inclined plane A B, the momentum 
will be so great as to overcom.e the resistance of the block. 
In the former case, b vvould only have to resist the weight 
of the ball a ; in the latter, it has to resist the iceight multi- 
plied into its velocity. You will therefore rem.ember that 
the momentum of a body is 'proportioned to the product of its 
quantity of matter and its velocity. 

EXAMPLES. 

125. Suppose A weighs 50 pounds, and moves at the rate 
of 20 feet in a second ; B weighs 100 pounds and moves at 
the rate of ten fest in a second ; what are their momenta ?* 
50 multiplied by 20 is 1000 ; 100 multiplied by 10 is 1000; 
therefore their mom.enta are equal, being both represented 
by 1000. 

In this example we see that a smaller body moving with 
a greater velocity, has a momentum equal to a larger body 
moving with less velocity. 

126. Suppose A weighs 15 pounds, and moves with a ve- 
iocity of 5 feet in a second ; B v*eighs 12 pounds and moves 
with the velocity of 6 feet in a second : what are these mo- 
menta 1 momentum of A. 15 X 5 = 75 

of B. 12 X 6 = 72t 

127. The momentum of bodies may then be calculated by 
the very simple rule of multiplication. A ball A weighing 
2 pounds, and moving with a velocity of 6 miles an hour, 

* Momenta is the plural of momentum. 

f X is the sign of multiplication, = of equality thus: 12 X 6 
= 72, signifies that 12 multiplied by 6 equals 72. 



Definition of force. To what is the momentum of a body proportioned 1 Ex- 
ample 1st. Equ;il momenta of unequal weights. Example 2d. Rule for 
tcilculatinsr momentum. 



MOTION AND FORCE. 51 

will strike with a momentum wliich may be represented by 
tiie product of two multiplied by 6, viz., 12 ; and a ball, B, 
weighing 6 pounds and moving with the velocity of 8 miles 
an hour, will have a momentum equal to these two numbers 
multiplied together, viz. 4S. — In comparing the momenta of 
the two balls, we have only to divide the greater by the 
smaller number ; thus 48 divided by 12 gives 4, so that the 
momentum of B is four times that of A, or in other words, B 
moves with four times the force of A. 

128. When two bodies of equal weight meet, the shock 
is the same, whether the motion be shared between them, or 
be wholly in one : — but where their weight is different, the 
shock is greater to the smaller body. If one person run 
against another who is standing, both receive a shock. If 
both be running at the same rate, in opposite directions, the 
shock is doubled. In some eases, as m swift skating, when 
the velocity is very great, the momentum has been sufBcient 
to destroy the lives of those who have thus met. " When 
two ships in opposite courses meet at sea, although each may 
be sailing at a moderate rate, the destruction is often as 
complete to both, as if with a double velocity they had struck 
on a rock. Manj^ melancholy instances of this kind are on 
record. In the darkness of night, a large ship has met one 
smaller and weaker, and in the lapse of a few seconds, have 
followed the shock of the encounter, the scream of the sur- 
prised victims, and the horrible silence v/hen the waves had 
again closed over them and their vessel forever. In No- 
vember, 1825, the Comet steamboat v/as thus destroyed, and 
carried to the bottom with about seventy passengers, into 
whose ears the drowning water rushed before the sounds of 
arrested music and joy had died avv^ay."* 



-" Aniott's Elements of P' 



lysics. 



Shock caused by the meeting of bodies ia motion. 



52 NATURAL PHILOSOPHY. 



LECTURE VI. 

OF THE LAWS OF MOTION. 

129. There are three important principles of motion call= 
ed the laws of motion, which are of very extensive applica- 
tion in mechanical philosophy. 

First law of motion : A body continues always in a 
state of rest, or of uniform motion in a right line^ till com- 
pelled to change that state, hy some external force. 

130. This law of motion is the necessary result of the 
inertia of matter, which, we have already observed, resists 
any change of state, whether of motion or rest. You will 
recollect that we have named the resistance of the air, fric- 
tion, and gravitation, as forces which tend to stop motion. 
On account of the various obstacles which exist at the sur- 
face of the earth, we see here no instances of perpetual mo- 
tion ; but the heavenly bodies in their continued and unde- 
viating revolutions, shew the tendency of matter to continue 
in motion when meeting with no impediments. They move, 
not because they are impelled by any new force, but from 
the original impulse which first called them into action. 

131. A body at rest requires more force to produce mo- 
tion, than would be required to keep the same in motion. 
Thus we often see a horse appear to start a heavy load 
with difficulty, but move on with little effort after the resist- 
ance of rest has been once overcome. In large bodies mo- 
tion should be applied gradually, or it may affect only a part 
of the mass, and thus break it by destroying its cohesion. 
Thus if a team with a heavy load, be suddenly started for- 
ward, there is danger that some part of the harness may be 
broken. The child who draws with a string his little cart, 
soon learns that when he has a load upon it, if he does not 
pull with a gentle and steady force, his string will be in dan- 
ger of breaking. 

First Law of motion. No perpetual motion on the surface of the earth. Per- 
petual motion of the heavenly bodies. Resistance of rest. 



OP THE LAWS OP MOTION . ^3 

132. The effect of inertia with respect to bodies in motion 
is no less striking than with respect to rest. If a ship saiKng 
with only a moderate velocity, suddenly stops, the passengers 
within, to whom the motion had not been perceptible, experi- 
ence a sudden shock, and the movable furniture is thrown 
forward. Should the earth be suddenly stopped in its diurnal 
motion, every thing on its surface would be thrown eastward or 
in the same direction towards which the earth was revolving. 

Fig- 14. On the same principle, if, while 

a person is riding swiftly on 
horseback, the horse suddenly 
stop, the rider is liable to be 
thrown forward; while the 
sudden starting forward of a 
horse may throw the rider 
backward ; the former case 
proves the inertia of motion, 
the latter of rest. A skater 
*' moving with swiftness sudden- 
ly sees directly before him a dangerous break in the ice, but 
the power of the will is not sufficient instantly to overcome the 
inertia of motion, and his body moves forward into the open- 
ing chasm. 

Second law of motion. The motion of a hodi; is -a 
the direction of the force which produces it, and is pi^opor- 
tional to that force, 

133. 1st. Thdii motion is in the direction of the force im- 
pressed, is understood by the boy who throv/s a stone op- 
wards, to knock an apple* from a tree, or who strikes his 
ball with the wish of driving it to any particular point. 
Now if another boy wishes to turn the same ball out of its 
intended course, he understands, without knowing any thing 
of the theory of philosophy, how to effect this, by striking 
a side blow which shall give the ball an oblique direction. 
A wind blowing to the south impels light bodies in the same 
direction. The sportsman levels his gun, and the shot moves 

* The apple being detached from the free by the momentum of the stone, is 
brought to the ground by a new power, viz ; gravitation. 




The resistance of motion. Second Law of motion. Motion in the diroctio'i .^f 
the force impresssd. 

5 * 



54 NATURAL PHILOSOPHY. 

exactly in the direction he intends, or in that which the ex- 
pansive force of the gun-powder impels it. 

134. 2d. Motion is proportional to the force which produ- 
ces it. To throw a ball weighing two pounds a distance of 
ten feet, requires twice as much force as to throw a ball 
weighing one pound the same distance : or, a ball of one 
pound weight moves twice as fast as a ball of two pounds 
weight, if both are impelled by the same force. Again, if 
two balls of equal v/eight are impelled, the one with a force 
twice as great as the other, the quantity of motion of the one 
will be twice as great as that of the other. 

A man by exerting his strength, (which is here the force 
used) might, with a rope, drav/ a small skiff to shore very 
quickly ; a loaded barge would with the same force move 
slowly, and a large ship with scarcely a perceptible motion. 

135. Third law of motion. To every action of one 
body upon another, there is an equal and contrary reaction ; 
or when a body communicates motion to another, it loses of 
its own momentum, as much as it imparts. 

136. If a man in one boat pull at a rope attached to anoth- 
er, his own boat will be moved by the force which he uses ; 
if the two boats be of equal size and load, they will both 
move at the same rate, and meet half way from the places 
from which they started. If a man in a small boat, should 
attempt to pull towards him a large ship, his own boat would 
move with a velocity greater in proportion as its weiglit is 
less than the ship ; but if in a large ship he should draw 
towards him r. little boat, the ship itself would be reacted 
upon and move, although not enough to be perceptible to 
the senses. You will the better understand this, by suppos-, 
ing that if the resistance of the ship were one thousand times 
greater than that of the boat, a thousand men in as many 
boats, all pulling together in one direction would make the 
ship meet them half way. A boatman pushes oif his boat 
by pressing with his oar against the land, the force reacting 
in the opposite direction ; and by a continued succession of 
back strokes, and the reaction of the water upon the boat, it 

Motion proportioned to force. Third Law of motion. Action and reaction. 




OF THE LAWS OP MOTION. 55 

15. is moved forward. The bird flies 

^ - ,^:^.upward by striking the air with his 

..^P^ wings, in a downward direction, 
the air reactmgupon his body, rais- 
es him at each stroke. In flying 
through the air in a horizontal di- 
rection, the stroke with his wings 
would be backward, like the strokes of a boatman with his 
oar. 

137. A man in swimming, by pressing the water down- 
wards and backwards with his hands, is borne upwards and 
forwards by the reaction of the water. The cripple setting 
his crutches upon the ground, receives a reacting force in 
his arms which thus perform a part of the whole labour of 
walking. 

Fig. 16. 138. A boy laid a wager, that he could 

t :ifeMiii M^^^^^ lift himself up in a large basket, by taking 
ij: hold of the handles ; if he had learned that 
liiji action and reaction are always equal and in 
'1. contrary directions, he would have perceived 
i, ..ithat the thing must be impossible, since what- 

mever force he exerted would be wholly ex- 
pended upon himself, Vv^ithout moving the basket. Thus a 
person with his hands clasped under his feet, might vainly 
attempt to raise himself from the ground. The downward 
force is not only equal to the upward, but is exerted directly 
against it, so that they counteract each other. In the two 
last instances we have given, action and reaction mutually 
destroy each other, of course no motion is produced. 

The third law of motion, viz : that action and reaction 
are equal and contrary, may be illustrated by the percussion 
of elastic and non-elastic bodies. 

139. By percussion, is meant the collisionf or striking to- 
gether of bodies. 

140. Elastic bodies, are those which, after compression, 
i eturn to their former state. If bodies have the power of 
restoring themselves immediately after compression, or pos- 
sess a force equal to any compressing power, they are said 
to be perfectly elastic. Air is an example of this ; a blad- 

Swimming ; walking on crutches. Action counteracted by reaction. Ho\r 
raay the third law of motion be illustrated ? Percussion. Elastic bodies. 



56 NATURAL PHILOSOPHY. 

der filled with air, after being compressed, will immediately 
expand to its former bulk. Solid bodies which will retain no 
permanent bend, are highly elastic, as marble, steel, and 
glass. 

141. A good steel sword may be bent until its ends meet, 
and yet return to its former state on being released from the 
force by which it was bent, but bad steel is not thus elastic, 
A pane of glass may be bent, but will instantly spring back. 
Indian rubber is highly elastic, though not perfectly so, for 
after being frequently stretched, it will appear to have lost 
something of its power to resume its former state. A ball 
of wool, cotton, or sponge, when compressed, exhibits the 
property of elasticity. 

142. Non-elastic bodies, are those destitute of the elastic 
spring, and when one strikes another, they do not rebound, 
but move on together after the stroke. Lead, clay, and un- 
raised dough, are non-elastic. 

Fig. 17. 143. Suppose a and b, to be two non- 

,^]\ elastic balls, suspended at c by threads of 

equal length, so that they may be in con- 
tact when at rest ; and let d e he a. gradr 
uated arc, over which the balls may move; 
then if the ball b, be moved a certain num^ 
ber of degrees towards e, and let fall so 
/rjY^jjXr^-jnfr^^ that it will strike the ball a, it communi- 
^^•^"■^^^TOp^-^^cates to the latter, half its momentum, and 




d % 



aT) both balls will move towards cZ, through a 

fiumber of degrees proportioned to their common velocity ; 
that is half as far as the ball b would have moved if it had 
met with no obstruction ; but as the two balls containing twice 
-the quantity of matter, are now moved by the same force 
which impelled b, it follows that the velocity is diminished in 
ihe same proportion. 

144. If two non-elastic bodies of equal weight and veloci- 
ty strike against each other, the momenta of both will be 
destro5^ed. Suppose that the two bodies, A B, have equal 
weight and velocity, and of course equal momenta ; moving 
in opposite directions, they meet at C, by which stroke the 

Steel, glass, &c., elastic. Non-elastic bodies. A non-elastic ball in motion, 
foiling against one at rest. Meeting of two non-elastic balls in motion. 



OP THE LAWS OP MOTION. 



57 



momenta of both balls is destroyed, and they remain at rest, 
as seen at D and E. 

Fig. 18. 
C 



D 



E 



iB 



Pi?, n 



145. When two perfectly elastic bodies, of equal weight 
and velocity, strike against each other, the striking body com- 
municates the whole of its motion to the other, dud then re- 
mains at rest. 

Thus, suppose two ivory balls of equal 
weight, a b, be suspended by threads, 
let a be drawn aside to c, and then let 
fall against b, it will drive it to d, or a 
distance equal to that through which a 
(Qihad fallen, while the latter having im- 
^ parted all its motion, remains at rest as 




at a. 



Pier 




146. Or suppose six ivory 
balls of equal weight, to be 
suspended by threads, and the 
ball a be drawn aside and 
then suffered to fall against c, 
the latter will communicate 
its motion to c and then stop. 
Thus each ball will succes- 
sively transmit its motion to the next and remain at rest, 
while the last ball b, will move off to B with the original ve- 
locity of a. 

147. The pupil may be somewhat doubtful with respect 
to the elasticity of balls of ivory and marble, since he can- 
not compress them with his hand, as he can an Indian rubber 
or cotton ball, nor perceive the compression made upon them 
by their colHsion with hard bodies. But an ivory letter- 
folder, or riding stick, is manifestly elastic, since, when bent, 
it springs back as soon as the force is withdrawn. That 
both ivory and marble do yield by collision, is proved by a 



Two elastic balls striking against each other. Example. Motion couiumni^ 
cated to several elastic balls. 



gS NATURAL PHILOSOPHY. 

very simple experiment ; if an ivory ball fall upon a mar^ 
hie slab, it rebounds (owing to the elasticity of both bodies) 
nearly to the height from which it fell, and no mark is left 
on either ; but let the marble slab be wet, and it will be seen 
that both bodies had yielded at the point of contact, from the 
fact that a circular surface of some extent is found dried by 
the blow. Billiard balls retain their perfect form, and even 
their polish, for a long time, although they are, in reality, 
indented at every stroke, but from their great elasticity, the 
compressed parts instantly spring back. Sealing wax re- 
tains the impression of the seal because it has no elasticity, 
or power to spring back after the resistance is removed* 
Figures can be stamped on soft clay, and dough, for the 
same reason. In raised dough, however, owing to its pores 
being filled with an elastic fluid,* there is much elasticity. 

148. One of the tricks of jugglers is to exhibit a man, 
bearing, unharmed, heavy blov/s given with a large ham- 
mer or sledge, upon an anvil lying on his breast. It is 
plain, that the same blows received upon the breast, would 
kill the man, and the additional weight of the anvil might 
seem to increase the danger ; but, in reality, the quantity of 
motion in the hammer is diffused through the great mass of 
the anvil, and produces but a small shock upon the chest, 
which, being itself elastic, easily resists the blow. 

149. If a non-elastic body strike upon an immovable ob- 
stacle, it icUl lose all its motion. For example : let a ball 
of lead, or of soft clay, fall upon the floor, and it will stop 
without any rebound. 

150. If an elastic body fall iipo7i an immovable obstacle^ 
it will rebound with a force equal to the stroke, and in a con- 
trary direction, thus exemplifying the third law of motion, 
that action and reaction are equal, and in contrary direc- 
tions. 

151. If a ball of ivory, or any other elastic substance, be 
dropped perpendicularly upon a marble slab, or other hard, 
immovable body, it will rebound in the same straight line 
in which it fell ; but if thrown obliquely, it v.ill not rebound 

* Carbonic acid gas. 

• Ivory and marble proved to be elastic. Juggler's feat explained. Non-elastic 
body falling against an immovable object. An elastic body fulling against an im- 
.movable object. 



OP THE LAWS OP MOTION. 



59 




in the same line by which it first 
moved, but as obliquely on the oppo- 
site side. Suppose an elastic ball a, to 
fall upon a hard substance h ; if it fall 
perpendicularly, or in the line a h, it 
will rebound in the same perpendicular, 
or in the line b a ; but if it fall in the 
I direction c b, it will rebound in the line 
b d. Now c J is the line of incidence,* and rf 6 is the line 
of reflection, f and the more oblique or slanting the former 
line is, the more so will be the latter. The perpendicular 
line a h\ divides the angle made by the lines of incidence 
Fig. 22. and reflection into two parts or 

f';||||fl|f,ii::;--- :-,. i^'#i);i|;i|i!!%!iiv angles, and these angles are 
equal, from whence it follows 
I hat the angle of incidence is 
always equal to the angle of re- 
flection. The boy who throws 
i:is ball upon the pavement, or 
;be floor, if he disregard this 
]aw of reflection, may chance 
to see a glass window broken 
by its rebound. Sound and 
light are reflected in the same 
manner as solid elastic bodies ; this we shall hereafter notice 
more particularly. 




* Incidence is from the Latin incideiis, which means a falling upon. 
t Reflection, from the Latin re andjlecto ; signifying to throwback. 

-jj i It may be well Jiere to explain, 

that though, in general, we mean by 
a perpendicular line, one that falls, in 
a right line towards the centre of the 
earth ; in geometry, any line whicli 
makes right angles with another line 
IS said to be a perpendicular line ; aid 
in this sense, the line A B, falling 
upon CD, or the wall of an apartment, is a perpendicular line, although, com- 
monly speaking, a line in that direction would be horizontal. 



Elastic balls falling perpendicularly. Angles of incidence and rcilection equal 



^0 NATURAL PHILOSOPHY, 

LECTURE VII. 

COMPOUND BIOTION. 

152. Simple motion is that which arises from the action 
of a single force, as any! ight substance floating in water or 
lying on smooth ice, is driven in the direction towards which 
the wind blows. A stone thrown by the hand moves towards 
the point aimed at by the one who throws it ; but strictly 
speaking, there is no example of simple motion, since in the 
absolute motion of all terrestrial bodies, is combined that of 
the earth, in its diurnal and annual revolutions. 

Composition of Forces. 

153. Compound motion is that which is produced by 
several forces acting in different, but not in opposite direc- 
tions. 

154. If forces v/ere equal, and their directions exactly 
opposite to each other, the body acted upon by them would 
not move at all ; so if the human mind be acted upon by 
equal and opposite motives, the person, according to meta- 
physicians, would not act at all. 

155. When two forces (not in direct opposition) act upon 
a body at the same time, as it cannot move two ways at once, 
it holds a middle course between the directions of the separate 

forces. This course is called the resulting direction, or re- 
sultant, because it results from the composition or union of 
the forces. 

Fig. 23. 156. Suppose a ball A, to be at the 

same instant struck by two equal forces 
■^ X and Y, the former moving in the di- 
rection B,and the latter in the direction 
C,the force X alone would have sent the 
bail to B, and the force Y would have 
sent it to C ; but the joint action of 
the iwo forces will cause it to move in 
a diagonal line at an equal distance 

Simple motion. Compound motion. Equal and opposite forces prevent mo- 
lion. Proposition. Resulting- direction. Example of motion caused by two 
equal forces. 





COMPOUND MOTION. 61 

between them. If you draw a line from B, parallel to AC, 
and another from C parallel to A B, the two lines will meet 
in the point D, vrhere the ball would stop. The figure 
A B D C is a square, and the line D A is, therefore, the di- 
agonal of a square. 

157. In t,he example above given, the moving forces were 
equal ; but suppose that the force X were twice as great 

- as the force Y ; in this case it 

^=' ' Y would drive the ball twice as far, 

consequently the line A B (the 
X distance to which the ball A 
would be driven by the force X) 
would be twice as long as the 
^ c line A C (the distance to which 

the ball would be driven by the force Y). The body, acted 
upon by the compound forces, would move in a diagonal line 
between the two ; and by drawing a straight line from B 
parallel to A C, and another from C, parallel to A B, they 
will meet in the point D, and the line D A is the diagonal of 
a parallelogram whose length is double its breadth. 

158. The different forces act with greater power upon the 
moving body, when the angle at which they meet is acute ; 
as in this case they approach nearer to a union of forces, 
hence the diagonal or resultant fas the line produced by the 
moving body is called) will be longer, as may be seen in 
the line A D of the parallelogram A B D C (as in fig. 24.) 
By rendering the angle BAG smaller, the diagonal or re- 
sultant would be still longer, because the joint impression of 
the forces would be increased ; therefore v/hen this angle 
should entirely disappear, or in other words, when; the sides 
A B and A C should coincide with the diagonal A D, the two 
forces would act in the same direction, and the moving body 
have the full effect of their joint forces ; but this would cease 
to be an example of the composition of forces ; it would be 
the junction or union of two forces. 



Motion caused by two unequal forces. Compound forces acting at an acute 
angle. 

' 6 



62 



NATURAL PHILOSOPHY. 




159. Again, if the angle made b^v' 
the direction of two forces be very 
obtuse, as in the angle BAG, they 
approach nearer to an opposition of 
forces, and the diagonal or resultant 
A D is proportionally shortened. 
When the forces represented by the 
D c lines A B and AC, meet without 

forming any angle, provided they were equal forces, they 
would act in direct opposition and destroy each other, con- 
sequently the body at A, upon which they would act, would 
have no motion. But if one force were superiour to the other, 
the body would not move in a diagonal line, but in the direc- 
tion of the greater force. 

160. When a body wopld describe the tico sides of a tri- 
angle by two forces acting separately, it will in the sametime 
describe the third side hy the two forces acting jointly. Thus 

a boatman wishing to cross 

D a river from A to C, 

y — would steer his boa^ di- 



X rectly towards B, so that 

/ his own force combined 

/ with the force of the 

stream acting from E to 

B c F A, or B to C, would cause 

the boat to describe the diagonal A C. The force of the 
stream alone would carry him from A to D, his own 
force alone would, in the same time, carry him to B ; but 
the two forces compounded will carry him to C, the desired 
point.* The circus rider leaps over a rope when his horse 
is galloping at full speed, and comes down upon his saddle ; in 
this case he retains the motion which he had in common with 



Fig. 26. 
A 



* By a reference to Fig. 23, with the explanation, the pupil will easil}^ com- 
prehend how the parallelogi am AB C D is obtained, and will perceive that the 
t^hort diagonal A C, is made b\-ihe obtuse angle BAD, according to the illustra- 
tion of Fig. 25. 



Compound forces acting at an obtuse angle. Proposition. 



COMPOUND MOTION. 



63 




the horse, and descends not in a perpendicular but in an oblique 
direction, risuig in one diagonal 
line, and descending in another. 
U the horse were standing still, 
the motion of the rider in leap- 
ing up would carry him from A 
to B, but the motion of the horse 
would carry him directly for- 

^^__ ward, the diagonal between the 

two forces is thenlhe line E, by which he would rise, while 
he would descend in the corresponding line F through the 
joint effect of the force derived from the horse and his own 
weight, the latter of Avhich alone would cause him to sink 
in the direction C D or G FI. 

161. A stone dropped from the mast-head 
of a vessel, under sail, would be affected by 
the motion of the vessel as well as by the 
force of gravitation, and would therefore fall 
not in a perpendicular, but in a diagonal 
line. Let A represent the mast, S the stone, 
D the deck, and the line S E will be the dis- 
tance that the mast-head will have moved 
while the stone would have fallen, from the 
force of gravity alone, from S to the point 
under it on the deck ; but the stone, partak- 
I) ^ ing of the common motion of the ship, and 
impelled by gravity, takes a diagonal direction, and falls at 
the foot of the mast. 



Fig. 28. 

S ^E 

9 1 



Examples oftlie composition of forces. Stone falling from the mast-head of a 
vfssel. 



64 



NATURAL PHILOSOPHY. 




162. The navigator, in crossing the ocean, by observing 
Fig. 29. the course of his ship, is able to determine 
"^ the latitude and longitude. Thus if the 

course of his ship has been for a certain 
time south-west, then if D A and B C rep- 
resent parallels of latitude, and D B and 
A C, parallels of longitude, the diagonal line 
AB will describe the ship's course through 
the sea, and the difference of latitude and lon- 
gitude at particular points may thus be estimated. 

1683 Motion resulting from more than two forces. Bo- 
dies may be moved hy the action of more than two forces : 
A kite flying is acted upon by three forces, the string, the 
wind, and gravity ; or, which is the same thing, its own 
weight. The boy, that his kite may rise, first- balances it in 
Fig. 30. an oblique position in the 

l^ ^ air, then runs with it a few 

p'*™---."" "P^or I'ods, and the air, by its 

L '2':/:t§y^ ,„„.^ re-action, throws it up- 
wards. Let a h represent 
a kite in the air, in a slant- 
ing position, or inclined to- 
wards the surface of the 
earth at an angle of 45^*, 
and let ds represent the 
string. Suppose the wind to be blowing in the direction w d^ 
when it strikes the kite at d, it will be reflected in the direc- 





IX ' A B represents the surface of tiie" 
earth, C the zenith or point directlj^^ 
over head, a line drawn from which 
makes, with the surface of the earth, 
the angle C E B, or an angle of 90 
degrees. The line D E fo-ms A^th 
the same, the angle D E B of 4,| 
grees. 



Course of a ship indicatinc 
of three forces. 



latitude and longitude. Motion of a kite the resuli 



m' 



COMPOUND MOTION. 55 

tion- c^ o' ; and the force of the reflected wind reacting on the 
jiite in the opposite direction will tend to carry it perpen- 
dicularly towards h, but the wind is also acting on the kite 
with direct force, in the line lo d, tending to carry it horizon- 
tally towards k, while gravity is tending to bring the kite to 
the ground in the perpendicular direction dg; it is then 
acted upon in three directions, upwards towards h, by the 
reaction of the reflected force of the wind, sideways or to- 
wards Jc, by the direct force of the wind, and downwards or 
towards g by gravity. Now suppose the weight of the kite 
pull it downwards with the force of two pounds, and the wind 
act upon it upwards with a force equal to two pounds, and 
horizontally with the same force, it is evident that it will 
move horizontally, since the two forces dg and d h, acting 
in opposite directions, would destroy each other, and leave 
the kite to be moved wholly by the force w d. But if the 
forces be unequal, that is, supposing the weight of the kite 
to be but two pounds, while the horizontal and upward force 
of the wind be equal to four pounds, the kite would then be 
impelled horizontally towards k, with a force of four, and 
upv/ards towards h, with the force of two pounds (half the 
upward force being lost by the opposing weight of the kite;) 
now let the line dk he made twice the length of d h to 
represent double the force ; then complete the parallelogram 
dhlk, the diagonal dl will represent the line in which the 
kite would move. 

164. By letting the string of the kite fall from the hand, 
the j^istance which it had oflered to the v/ind would cease, 
ani^Hken this resistance no longer existed, there could no 
lon^^ be any reflected motion ; and the kite after being 
^olong by the horizontal action of the wind, would be 
it to the earth by gravity. By holding the string very 
le horizontal force of the wind ceases to act upon 

ind the reflected force raises it perpendicularly. 

^hen a kite rises suddenly in aper])endicular direc- 
it the string having been pulled, it is because its re- 
is increased by an increased velocity of tho 

fen the kite descends without any slackening of the 
string, it is owing to a lessened force of the wind or a change 
in its direction. 

Effect of increased or diminished velocity of the wind upon the kite. 

6* 




66 



NATURAL PHILOSOPHY. 



Fig. 31. 



166. From the examples we have given, the pupil will 
now understand the meaning of the terms so common in phi- 
losophy, viz. ; composition and resolution of forces, for it 
has been proved that any two or more forces or motions may 
be compounded into a single force, and move a body in a 
given direction ; also that any single force or motion may 
be resolved or decomposed into the forces which produce it. 
That is, when any force or motion is given, it is easy to find 
the forces in any other directions of which it is the resul- 
tant. 

167. The sailing of a boat is 
an instance of a body moving by 
the action of several forces. Let 
a h represent a boat, h c its rud- 
der, and s s the sail : suppose the 
wind to strike the sail in the direc- 
tion from e to w, it will be reflect- 
— ^ ed in the direction of w b, but the 
reflected wind reacts in a contrary 
direction, therefore the sail being 
acted upon by two nearly equal 
''^ forces, the one in the direction 

from 6 to ic, the other trom b to w, the body would take a 
course between the two, or towards d, were no resistance 
offered ; but the head of the boat being directed towards tz, 
the water presents a sideways resistance, so that thq^ryeal 
course of the boat will be tovv^ards g ; this deviation cgiused 
by the resistance of the water is called by seamen the leam^y. 
The rudder prevents the head of the vessel from ^Hng 
with the wind ; were it not for this, ships would be inc^BDle 
of being directed, and would be at the mercy of^fcrv 
wind. 




Composition and resolution of forces. Sailing of a 
composition of forces. 




ACCELERATED AND RETARDED MOTION. 57 

* 

LECTURE VIII. 

ACCELERATED AND RETARDED MOTION. 

168. Jjniform motion is that by which a ho^ 
dy passes over equal spaces in equal times, as 
the minute hand of a watch or clock, which 
in sixty minutes passes through a given cir- 
cle. The hour hand has also a uniform 
motion, though much slower, since it only 
passes through the twelfth part of the cir- 
cle, while the minute hand passes through 
the whole ; — the relative velocity of the 

hour hand is therefore twelve times less than that of the mi- 

nute hand. 

169. In order that a body should move with uniformye- 
locity, it is necessary that the power which set it^^^iotion 
(called the motive power) should cease to operate the mo- 
ment it has 'imparted that velocity, or that there should be a 
uniform force exerted to continue the motion ; thus a ball 
thrown forward with one impulse, would forever proceed on 
in one straight line, with a uniform motion, did not gravity 
and the resistance of the air retard its motion, and at length 
cause it to stop. 

170. The uniform motion of a watch is produced by a 
force (the spring) acting upon the wheels in a steady and 
uniform manner : a horse, moving at the rate of six miles 
an hour, goes with a uniform velocity, which is caused by 
the continued exertion of muscular strength. 

171. A body, descending by gravity, is not acted upon 
merely by one impulse, but by a continued series of im- 
pulses, each added to the previous ones. If a ball, rolhng 
upon smooth ice, were every instant to receive a new stroke, 
thus retaining all the previous momentum, and continually 
receiving more, its velocity would soon become very great. 
Thus a falling body is continually receiving new velocity 
and momentund. 



Uniform motion. What would produce uniCorni motion'? Examples 
nniform motion. Falling bodies continually acted upon by new impulses. 



68 NAT URAL PHILOSOPHY. 

Spaces described ^ Falling Bodies, 

172. The spaces described by bodies falling from a state 
of rest by the influence of gravity, are as the squares of the 
t^mes in which they are falling, 

173. A stone falling from a high tower, will, in two se- 
conds. Ml four times as far as in one second ; in three se- 
conds, nine times as far ; in four seconds, sixteen times as 
far-; and in ten seconds, one hundred times as far; be- 
cause the square of 2 seconds is 4 ; the square of 3 is 9; 
of 4 is 16, and the square of 10 is 100.* 

174. It has been proved that a body falling from a state 
of rest, passes through 16 feetf the first second of time, in 
two seconds it would then pass through 4 times 16 or 64 
feet, and in three seconds (because we multiply by 9, which 
is the square of 3), it would pass through 144 feet, and in 
ten seconds (because 16 is multiplied by the square of 10) 
1600 feet. Therefore to find the number of feet through 
"which a body has fallen, the time being known, multiply the 
square of the number of seconds hj 16. 

Example. Suppose a body to have been falUng five se- 
conds, through what space has it fallen ? 
• Answer. 400 feet, which is 16 multiplied by the square 
of 5. 

Velocity of Falling Bodies, 

175. If a body, having fallen through a certain space, 
should receive no farther impulse from gravity, but should 
proceed on uniformly with the last acquired velocity, it would 
describe twice the space in the same time as that during which 
it had fallen to acquire that velocity. 

176. Suppose a body, at the end of one second, to have 
fallen 16 feet, it would have acquired a velocity, which in 
in the next second would carry it 32 feet ; at the end oifour 
seconds, its space, multiplying 16 by the square of 4, being 

* The square of any number is that number multiplied by itself, 
t 16 feet and one inch is the exact distance through which, it is proved, a 
body falling freely by gravitation, passes the first second of its descent. 

Proposition. Example. Rule for finding the number of feet through which 
a body falls in a given time. Elxample. Proposition. Example. 



ACCELERATED AND RETARDED M0TI0N. ^9 

256- feet ; the next four seconds it would descend 512 feet, 
ov^twice ilie space in the same time as that during which it 
liadjallen to acquire that velocity. 





A 


Fig. 33. 




1 


a\\'c\'y\\ \l "'"•., 


3 




r\ 


D '■■■■, i • '"\ ; "■•■-. 


3 






\ 


>-S\ 


4 






l\ 


J\iF '■■■ 


5 


3\ 








1 

7^. 



Time, Space and Velocity. 

177. Let the hne A B repre- 
sent the TIME in which a falling 
body descends divided into se- 
conds ; the horizontal lines 1 C, 
2 D, 3 E, 4 F, and 5 G, repre- 
sent, by their increasing lengths, 
the VELOCITY acquired in each 
second, that is, the velocity in- 
creases as the lines increase in 
G length. The small triangles 
represent spaces ; by multiply- 
" " ^ ing 16, the number of feet iri 

which a body falls the first second by the number of trian- 
gles in each line, we learn the space passed through in each 
second. In the first second we have one triangle «, in the se- 
cond second we have three triangles, J? cd, in the third second 
we have five triangles, efg, &c., in the fourth second we have 
seven triangles, j A: /, &cl, and in the fifth second we have 
nine triangles, ^r 5, &c., the spaces in each successive 
second increasing in proportion to the series of odd numbers, 
1, 3, 5, 7, 9, &c. That is, during the first second, ihe body 
falls a certain distance, say 16 feet ; during the next second 
it falls three times as far; during the third, five times as 
far ; during the fourth, seven times as far ; during the fifth, 
nine times as far, and so on in the same proportions. These 
odd numbers, 1, 3, 5, &c. are the ratios or proportions in 
which the velocity of falling bodies is uniformly accele- 
rated. 

178. Now, if a body fall 16 feet the first second, during 
the next il*will fall 16 feet multiplied by 3, that is, 48 feet ; 
in the third second it will fall 80 feet, or 16 multiplied by 
5, &c. 

How are time, space and velocity expressed in the figure ? What are their 
mutual relations? Method of calculating the space passed throvigh by a fulling 
body in any separate second. 



7Q NATURAL PHILOSOPHY. 

Example. Through how many feet would a body descend 
the fifth second of its fall ? 

Answer. 144. MuUipiy 16 by 9, because the body falls 
nine times as far during the fifth second as during the 
first. 

179. But if it be required to show the whole space through 
which a body has fallen during five seconds of time, you 
have (according to a rule already given) to multiply 16 by 
the square of the time ; the square of 5 being 25, the answer 
would be 400 feet. 

180. The reason for expressing the velocities of falling 
bodies by the ratio of odd numbers may be briefly given. A 
bod}- falling by the impulse of gravitation descends 16 feet 
in the first second ; but having received an accession of 
motion during the whole of this second, it is moving more 
rapidly at its close than at any previous time With that 
motion alone, if it continued uniform, it would in the next 
second descend through twice 16, or 32 feet ; but during 
this next second, as much motion is conimunicated as 
during the first ; therefore the body descends 3 times 16, 
or 48 feet. The whole of this accumulated motion would 
now carry the body through 4 times 16, or 64 feet ; in 
the third second, gravity alone vvould carry it 16 feet; 
and the last number being added to 64, we have 5 times 
16, or 80 feet, for the space passed over by the body in 
the third second. The motion now accumulated would, 
in the fourth second, cause the body to descend 6 times 16, 
or 96 feet, and gravity alone would also carry it 16 feet, 
which, being added, make 112, or 7 times 16 feet, the space 
through which it would fall during the fourth second. For 
the fifth and succeeding seconds, we should proceed in the 
same manner, thus obtaining the series of odd numbers 
which express the distances passed through in successive 
seconds. 



Whole space through which a body falls within a given numljer of seconds. 
Why the increase of the velocity of falling bodies is expressed by the series of 
odd numbers. 



ACCELERATED AND RETARDED MOTION. 



181. The following table may illustrate this subject. 



71 



Seconds of de- 
scent. 
1 


Feet passed through 

at the end of each 

second. 

16 


Final velocity in 
each second. 

32 


Feet passed through 
during each second, 

16. 


2 


64 


64 


48. 


. 3 


144 


98 


80. 


4 . 


258 


128 


112. 


5 


400 


160 


144. 



182. The first column of figures stands foY the time of 
descent of a falling body? as divided into seconds. 

183. The second column of figures shows the whole num. 
her of feet through which the falling body has passed at the 
end of each second ; and these numbers are obtained by mul- 
tiplying 16 by the square of the figure in the first column, 
according to the following rule ; the whole spaces jMssed 
through are proporfio?ial to the squares of the whole times, 

184. The third column of figures shows the final velocity 
in each second ; these numbers are obtained by multiplying 
16 by the even numbers 2, 4, 6, 8, &c. according to the 
following rule ; the velocity passed at the end of any num- 
ber of seconds, is represented hy tivice that numher multi^ 
plied hy 16 ; as the final velocity at the end of two seconds 
is 64; or 16 multiplied by twice 2. 

185. The fourth column of figures shows the feet passed 
through during each second ; the numbers are obtained by 
multipl3nng 16 by the series of odd numbers which repre- 
sent the ratio of acquired velocities, according to the follow- 
ing rule ; — the spaces through ivhich a falling body passes 
in a succession of equal intervals are in the proportion of 
1, 3, 5, 7, 9, 11, &c. ; the number of feet passed through 
in each second is 16 less than that of the final velocity, that 
is, the body has acquired during the last second of its fall a 
velocity which, without any new impulse from gravitation, 
would in the next second carry it 16 feet farther than it 
moved the preceding second. 

186. In all computations respecting the velocity of falling 



The first cohimn of figures. (See section 181.) The second column of figures. 
(See section 181.) The third cohimn of figures. (See section ISl.) The fourth 
column of figures. (Sec soction 181.) 



72 NATURAL PHILOSOPHY. 

bodies, the essential points are to know the space fallen 
through in one second, and the acquired vdocity during that 
time. The height of a tower or precipice, or the depth of a 
well or cavern, may be easily computed by marking the 
time in which a body falls from the top to the bottom ; or if 
the height or depth be known, the time in which a body would 
fall to the bottom might be ascertained. 

187. We have said nothing of the resistance of the air as 
impeding the velocity of falling bodies, though this has some 
effect, even in the heaviest substances. The calculations 
we have made do not, therefore, allov\' any thing for this re- 
sistance. By the expression " a body falling freely by 
gravitation^^'' you are to understand a body fulling in a 
vacuuiti. The pupil will recollect that it has already been 
proved, by the experiment of 9, piece of lead and a feather 
falling in an exhausted receiver, that the velocities of bodies 
falling from the same height are equal ; as the attracting 
force which acts' upon the greater mass will exceed that 
v/hich acts upon the less, as much as the greater body ex- 
ceeds the less in quantity of matter. 

188. The accelerated motion of falling bodies is familiar 
to every observer of nature ; — an apple falling from a tree, 
is at first visible to the eye, but its velocity is soon such that 
It ceases to appear a distinct object, and only the line of its 
descent is visible. 

189; A person on the summit of a precipice pushes to its 
sdge the t>agment of a rock, at first its speed is not very 
great, but it soon begins to move more rapidly, and gather- 
ing new velocity at every instant of its fall, rushes down- 
wards with tremendous force. Boys who are accustomed 
in winter to slide down a hill upon their little sledges are fa- 
miliar with the fact that the velocity acquired in their de- 
scent carries them on some distance after they have reached 
the foot of the hill, and even some way up an acclivity. 

190. When standing by a waterfall of considerable 
height, we may first see the water slowly descending in one 
sheet, but as the eye follows its downward course, we per- 
ceive the force and velocity becoming greater at every in- 
Essential points in computing the velocity of falling bodies. What i^meant 
b V bodies falling freely 1 Example of accelerated motion. A stone falling from 
a precipice. Boys sliding down a hill. Waterfall. 



ACCELERATED AND RETARDED MOTION. 73 

stant, until seen only as foam or mist, it dashes into the 
chasm below, and mingles with the current. 




191. Calculations respecting falling bodies 
have been rendered very accurate by means 
of a machine invented by George Atwood.* 
By means of this machine the descent of falling 
bodies is rendered so gradual, that the rela- 
tions between times and spaces, can be accu- 
rately determined ; for though the motion is 
retarded, these relations remain unchanged. 
The machine consists of a wooden column not 
less than ten feet high, with a rod marked by 
feet and inches, and two weights suspended 
over pulleys. The rapidity of the falling mo- 
tion in the heavier of the weights is retarded 
by the lighter weight, while the gradual in- 
crease is scarcely influenced, and may be seen 
by the eye as it descends along the graduated 
rod, while the seconds of time may be noted 
by listening to the beats of a clock. 



Retarded Motion. 

192. The ascending motion of bodies thrown upwards, is 
retarded in the same proportion as that of falling bodies is 
accelerated. The same laws that regulate uniformly accel- 
erated velocities, will, when reversed, apply equally to uni- 
formly retarded velocities. 

' Professor of Natrral Philosophy at Cambridge, England, in 1781. 



Atwood's machine. In what proportion is upward motion retarded ? 

7 . 



74 NATURAL PHILOSOPHY. 

Fig. 34. 
E — r- 



193. Suppose that a body thrown from A, perpen- 
dicularly upwards, moves with a force sufficient 
to carry it in the first second to B, in the second 
to C, in the third to D, and in the fourth to E, the 
motion which has been uniformly growing less, 
here ceases, and gravity, having now wholly over- 
come the projectile Jorce, operates without oppo- 
sition ; the body begins to fall, and at every in- 
stant receiving from gravity and velocity a nevv 
momentum downwards, passes through the same 
spaces in the same times as in its ascent ; that is, 
it falls from E to D in the first second, from D to 
C in the next, from C to B in the third, and from 
B to A in the fourth. 



194. The projectile force is that which impels the body^ 
and may be greater or less, as a bullet thrown upwards 
with the hand moves with little force compared to that which 
would be given to one shot upwards with a gun. In the 
former case the velocity would be less than in the latter, in 
proportion as the projectile torce was less, the space through 
which it would move would be less in the same ratio, and 
also the time which would pass before it reached the ground. 
If one body is shot upwards with twice the force of another, 
it rises twdce as high ; if shot with ten times the force it rises 
ten times as high. 

195. Suppose that an arrow> shot upwards from a bow, reach- 
es the ground in six seconds, how many feet did it ascend 1 

E plain the phenomenon of the fall of a body. Velocity depends on the pro- 
jceiile force. 



CURVILINEAR MOTION. PROJECTILES. 75 

The times of ascent and descent being equal, the arrow was 
three seconds in rising, and three in faUing. We have 
learned that in order to know the spaces described by a 
falhng body, we must multiply the squares of the time by 
the velocity, which in bodies falling by gravitation, is 16 feet 
the first second ; the square of 3 (the number of seconds in 
which the arrow was falling) is 9 ; this multiplied by 16 
gives 144, which is the number of feet the arrow fell, con- 
sequently it must have risen to the same height, that is 144 
feet. 



LECTURE IX. 

CURVILINEAR MOTION. PROJECTILES. 

196. Curvilinear Motion, or motion in curved lines, is 
the. result of two forces acting on a body ; by one of which 
it is projected forward in a right line, whilst by the other 
it is drawn or impelled towards a fixed point. When either 
of these forces cease to act, the body will move in a straight 
line. 

197. A stone whirled in a sling, is acted upon by two 
forces, that of the hand, which represents the projectile force, 
and that of the string, which causes its motion to describe 
the circumference of a circle ; but if the string were to 
break while the stone was thus whirling, it would fly oflT in a 
tangent, being then acted upon only by the projectile force. 

198. If a ball be made to revolve within a hoop, laid flat 
upon a table, it will manifest a constant tendency to escape 
from the circle in which it is moving, by pressing against 
the sides of the hoop ; it is evident that if the hoop were 
lifted up while the ball is revolving, the circular motion 
would be destroyed, and the ball would fly ofl*in aright line 



To what height must a body have ascended which reaches the ground in six 
seconds after it was thrown upwards ? Cause of curvilinear motion. Stone 
^/hilled in a sling. Ball revolving in a hoop. 



76 



NATURAL PHILOSOPHY. 



from that point where it was when set free, and this hne will 
form a tangent to the circle in which the ball had moved, 

199. Thus we find curvilinear motion to be produced 
by two antagonist powers ; the one which draws the mov- 
ing body toward the centre of motion is called the centvipe- 
ial^ force, and the other, which is constantly tending'To cirive 
it from the centre, is called the centrifugaI,-[ and sometimes 
the tangential force, because the line of its direction is that 
of a tangent to the circle. These two forces are also called 
central forces. 

200. It might seem that curvilinear motion when once 
commenced, would still continue, where the moving body 
was at liberty to pursue its own course. But motion in a 
circle is, at every successive instant, a hent motion ; that is, 
the circle is made up of an infinite number of straight lines, 
and a constant force is necessary to counteract the tendency 
of the body to pursue these straight lines. 

201. Suppose a body, a, 
to be projected in the direc- 
tion a h, and at the same 
time to be attracted with 
equal force by w, it will o- 
bey neither force,but rnove 
towards d in the diagonal 
of a parallelogram, whose 
sides a c, and a p are in 
proportion to the two for- 
ces a h and a w ; the body 
would now continue to 
move towards m, if its motion were not bent by some new 
force. But at d, the body receives a new impulse from w 
tending to carry it in the direction d w, it therefore describes 
a new diagonal d g, and we have a second parallelogram by 
producing the sides g f and ge; at g, a new impulse is 
received from id, and the body, instead of moving in a straight 
line towards i, describes a new diagonal, g k ; here a new 
impulse from w, bends the motion from the straight line k n, 




* From centrum, a centre, and peto, to tend towards, 
t Fronri centrum, a centre, and/wgzo, to fly from. 

Two powers which produce curvilinear motion. Motion in a circle a bent 
motion. Example of bent motion. Describe the fi^re. 




CURVILINEAR MOTION. PROJECTILES. 77 

and carries the body on in a new diagonal to 0. The di- 
agonals of the parallelograms, will be smaller in proportion 
as the intervals are less in which the attractive force w, acts 
on the body a, and when this force is constantly in action as 
in the following figure, a tvill be constantly turned from its 
tangential direction, and move in a curve line. 

202. The motion of the moon a- 
round the earth, is in a curvilinear 
line produced by the action of the cen- 
trifugal force A D, and the centripetal 
force B A,thelatter,whichisthe earth's 
attraction, operating constantly, causes 
the moon to describe the curved line 
B^ A C. 

203. We have already remarked that the centrifugal 
force, if not counteracted, would carry the moving body in a 
straight hne following the direction of that force, and you 
will of course perceive that the centripetal force, unless coun- 
teracted, would draw the moving body directly toward it- 
self, so that the moon, in the one case, would fly off into dis- 
tant regions of space, and in the other, would rush towards 
the earth with tremendous velocity. The earth itself, is 
upheld in its orbit or path through the heavens, by the har- 
monious actions of the same forces ; were the one with- 
drawn, our planet would dart off, like the comet, into un- 
known regions of space ; were the other suspended, we 
should be precipitated upon the sun, which by its magnitude, 
overpowers all less attractions, and causes the earth to re- 
volve around it in ceaseless regularity. 

204. The centrifugal force of bodies revolving in a cir- 
cle, is proportioned to their specific gravities. Thus if cork, 
water, and quicksilver be v/hirled together in a vessel, they 
will arrange themselves in the inverse order of their specific 
gravities. This experiment may be performed by suspend- 
ing a common pail, by a cord, from the ceiling of a room ; 

Moon's motion. Effect of the centrifugal and centripetal forces upon :ho 
motion of the heavenly bodies. .Effect upon the etji th if one of these foixes were 
withdrawn. Centrifugal for';e proportioned to specific gravity. 

7* 



78 NATURAL PHILOSOPHY. 

the cord having been twisted by the turning of the pail, when 
let go, untwists itself, and gives a rapid whirling motion to the 
pail. This revolution carries the heaviest bodjjviz. , the quick- 
silver, farthest from the centre of the vessel ; while the cork, 
or the lightest body, will be nearest the centre. If the pail 
contain water onljj the water, by the untwisting of the cord, 
will sink in the centre and rise towards the sides of the pail, 
or where the centrifugal force is greatest. Thus we see 
that the centrifugal force tends to make bodies recede from 
a central point. 

205. The centrifugal force is increased by increasing the 
velocity of a revolving body ; or to express the same propo- 
sition more definitely, the centrifugal forces are proportion- 
ed to the squares of their velocities. Thus if the velocity is 
increased four times, the centrifugal force is sixteen times 
greater ; if increased ten times, tiie centrifugal force is one 
hundred times greater. The revolutions of the pail, by the 
untwisting of the suspended cord, may be so rapid as to 
cause a small quantity of the water, not only to rise to 
the edge of the pail, but to be thrown off, in straight, or 
tangent lines. 

206. If a pair of tongs be suspended in the same man- 
ner as the pail, and made to turn by the untwisting of the 
cord, the legs will separate with a force proportioned to the 
velocity of the rotation ; and when this rotation ceases, will 
resume their former situation. An application of this prin- 
ciple to mechanics, is seen in the regulator, an importan-: 
invention for regulating the supply of steam in steam en^ 

Regulator. gincs. It consists of two heavy balls 

^h a, connected with a perpendicular 
shaft s, in such a manner as to be ca- 
pable of falling parallel to the shafi 
when at rest, but when made to re- 
volve by the motion of a common ax- 
is., the balls diverge by the centrifu- 
gal force. By connecting the gov= 
ernor at c, with an important part of the steam engine, call- 
ed ihefly wheel, it is made to partake of the common mo- 
tion of the engine, and the balls will remain at a certain dis- 



Centrifugal force proportioned to velocity. 




CURVILINEAR MOTION. PROJECTILES. 79 

■tance from the perpendicular shaft, while the motionis uni- 
form ; but when by an increase of steam, the motion becomes 
more rapid, the balls will diverge farther from the perpen/^ 
dicular, and in so doing, raise a valve connected with the 
boiler, by which such a portion of steam is let off as will 
suffer the balls to resum.e their usual position, which indicates 
that the velocityof the motionis reduced to the rate required. 
207. If a ball of soft clay. A, be made to re- 
volve rapidly upon an axis, it expands at the 
middle and becomes flattened at the two ends as 
at'B. This is because the middle, being farther 
from the axis of motion, has a greater velocity, 
and of course a greater centrifugal force. Now 
suppose the ball A to represent the figure of the 
earth as it was when it first began to revolve on 
its axis, and B to represent its figure as it exists 
at present. Like B, it is elevated at the equator 
and flattened at the poles.* The present figure of the earth 
is that of an oUate spheroid. A spheroid differs from a 
sphere, or globe, in being flattened in one direction and 
lengthened in another ; an orange is an ohiate spheroid, but 
a lemon, being elongated towards the ends, is a prolate 
spheroid. 

208. It has been proved by accurate calculations upon 
the nature of centrifugal force, that if the revolution of the 
earth on its axis were but seventeen times faster than it 
now is, bodies at the equator would be acted upon by this 
force as much as by gravity, in which case they would have 
no weight ; a little more velocity would cause them to riee 
and form a ring round the earth like that which surrounds 
the planet Saturn, or to fly off in pieces which might re- 
volve around the earth like so many little moons. 

' This fact is a strong evidence in favour of the Wernerian. theory of geolory, 
that the materials wliich compose the eartli were once in a fluid state, as the glebe 
•must have been like the ball of soft clay, in order thus to have been flattened «t 
the poles. 



Square of a sphere altered by centrifugal force. Cause of the earth's being 
flattened at the poles. Eflfects vvhicii would be produced if the earth's motion on 
iis axis were increased. 



so 



NATURAL PHILOSOPHY. 




209. Lest you should find difficulty in comprehending how 
one part of a revolving body moves with greater velocity 
than another, we will illustrate the subject by the motion of 

Fig. 38. a vv^heel ; you will perceive by the figure 

that in each revolution the circle to be 
described is small in proportion as it is 
near the axis of motion or centre of 
the wheel, which is itself at rest, and as 
the greater spaces are passed over in the 
same time as the smaller, it follows that 
the velocity must be greater in propor- 
tion ; and the centrifugal force increasing 
with the squares of the velocity, this force must be greatest 
at the rim of the wheel, or where the circle is greatest. 

210. By the axis of motion, is understood a line either re- 
al or imaginary round which a body turns ; if you put a wire 
through an orange, and turn the orange upon it, the wire is 
the axis of its motion. By the axis of the earth's motion, is 
understood an imaginary line through its centre, for in reali- 
ty the earth in its daily revolution turns without any axis , 
still a line through its centre is considered as its axis of mo- 

Fi<?. 39. tion. 

point 
on which it rests while revolving. 

'" Thus suppose that upon the table A D 

is fastened a string having at one end 
an ivory ball, B, to which a forward 
motion is given with the hand, it is 
evident that the ball will revolve in a 
circle, impelled by the action of the 
hand, which is the centrifugal force, 
and held by the string which is the 
j^ centripetal force, the point C is the 

centre of motion. 





D 




•-.. „ ! 






/ 


J© 


/ 


/ \ 


/ 


i 



The centre of motion is a 
round which a body turns, or 



Velocity least, nearest the centre of 2r-;otion, Centrifugal force greatest at the 
greatest distance from the centre of motion. Axis of motion. A:2is of the earth's 
motion. Centre of motion. 



CURVILINEAR iMOTION. PROJECTILES. 



81 



PROJECTILES. 



211. Any body thrown or projected, either obliquely, or 



horizontally into the air, is a projectile. 
Fig. 40. B 




Projectiles move in 
a curvilinear path, 
and the curve which 
they describe is called 
aparabola. Suppose 
a body to be thrown 
obliquely upwards in 
the direction A B, the 
force of gravity will 
begin to draw it to- 
wards the earth ; and 
as this force is every 
instant increasing the 
motion of the falling 
body, it will, at every instant, recede more rapidly from the 
line A B, thus describing the curve A C, which is continually 
deviating from the line of projection until it reaches the 
ground at C. 

212. The random of a projectile is the horizontal dis- 
tance between the points from which it is thrown, and that 
where it falls to the earth : thus the line A C (Fig. 40.), is 
the random of the projectile thrown in the direction A B. 

The mud thrown from a 
carriage wheel describes 
a parabola, as in the 
lines ac; ab are the 
straight lines in which the 
mud would move but for 
the force ofgravity,which 
brings it to the earth in 
the curved lines a c. 
218. A cannon ball shot horizontally over a level plain, 
will touch the ground as soon as another ball dropped at the 
same instant from the cannon's mouth ; for projectile motion 
does not at all interfere with the action of gravity ; that is. 




Parabola. Random of a projectile. Projectile motion docs not intcrlV 
gravity. 



with 



g2 NATURAL PHILOSOPHY. 

the body moving forward is going downward at every in- 
stant as rapidly as if it had no other than the downward 
motion. 

214. Suppose one stone to be projected directly forward 
from the top of a high tower, and another at the "U&me in- 
stant to be dropped directly downwards, both'^toMis will 
reach the ground at the same moment. 

215. If A D be the horizontal line of projection, and A B 
the perpendicular line of gravitation, then the stone which 

Fig. 41. is thrown forward will not 

D move in either line : but in 

A C, which is the result of the 

projectile force, and the force 

■■"! of gravitation combined, and 

*>.;,<?.., it would pass through the 

;\ ; space A a in the same time 

..J....':i^... that gravity alone would car- 

i \ ! ^ ry the other stone from A to 7; 

-'--■^; when, therefore, the one stone 

j\; is at h, the other is at 2 ; in 
' '■ hke mianner c corresponds to 



3, tZ to 4, e to 5, and^" to 6, also the stone which was thrown 
forward from the top of the tower touches the ground at C 
in the line A C, at the same instant that the stone which was 
dropped perpendicularly to the ground touches it at B. 

216. The study of projectiles has become an important 
part of military science. In firing at distant objects it is 
necessary that the engineer should not only know in what 
situation to place his cannon in order to give the required 
direction to the ball, but the velocity with which it will move, 
that he may thus calculate the curve which it will describe 
before it falls, and consequently the spot where it will strike. 
In cannonading a city, a great advantage is gained by an 
elevated position, as projectiles thrown from such a point 
take effect at a greater distance than if thrown from a level ; 
as a stone projected from the brow of a hill downwards, 
moves with much greater force, and consequently evermore 
space than if thrown by a person standing upon level ground. 
A cannon ball shot horizontally from the top of one of the 



. Ex=ia;ple of a body projected at the instant another is dropped downwards 
Demonstration. Cannonading a city. 



CENTRE OF GRAVITY, 



SB 



Fig. 42. 
P A 




highest points of the Andes would move three or four nniles 
before it fell. 

217. Suppose a body placed 
at the point A, above the surface 
of the earth ; if it were let to fall 
with no projectile force, gravity- 
would cause it to descend with 
an accelerated motion towards 
I the earth's centre in the perpen- 
'dicular direction AB. But if 
the body were impelled by a 
projectile force in the direction 
AP, it would descend in the 
curve line A D. The greater 
the projectile force A P, the greater will be the sweep of the 
curve line. Thus a greater degree of force would send the 
body to E, and a still greater degree of force would send it 
to F. If the velocity of projection were increased to a cer- 
tain amount, the body would reach the antipodes, and even 
continue its course round the globe until it returned to the 
point A, whence it started. Were it not for the resis- 
tance of the air, the projected body which would now move 
three or four miles before falling, v/ould go nearly forty 
miles, and could it be impelled with ten times the velocity of 
a cannon ball, the centrifugal and centripetal forces would 
be in equilibrium, or balance each other, and the body, by 
their mutual action, be kept revolving round the earth as a 
satellite. 



LECTURE X. 

CKNTRE OF GRAVITY. 



218. The centre of gravity is that point in a hodij, ahoui 
which, if supported, all the parts exactly balance each other. 
Therefore if a body be suspended or supported by the cen- 



In what case would a projectile revolve around the earth? 



g4 NATURAL PHILOSOPHY. 

tre of gravity, it will rest in any position, and whatever sup- 
ports that point bears the v/eight of the whole mass. 

219. Though in any mass of matter every atom has its 
separate gravity and inertia, and the weight and inertia are 
in reality diffused through the whole, yet as there is one 
point which, when supported, balances the whole, and when 
not supported, leaves the w^hole to fall, the weight of the 
body may be considered as centred at that point. 

220. In a body of a regular figure, and composed of a 
substance of uniform density, the centre of gravity is the 
same as the centre of magnitude, as in a cube of wood or a 
ball of lead ; where this centre of the cube or ball is, will 
be also the centre of gravity. In the following figures, the 
lines intersect each other in the centre of the figure, and 
supposing each to be of a uniform density, this centre is also 
the point where the quantities of matter are equal on all 
sides, and therefore exactly balance each other. 

Fiff. 43. 




221, It is evident that it must be important where there are 

bodies to be moved, to understand how to apply the force so 

as to act on this centre of gravity, for if the force be applied 

in a wrong direction, it would either have no effect or would 

Fig. .44. overturn the body. Suppose the figure to be 

]B a solid body, with a hemispherical base, and 

^— — — 3;^^^ that A is the centre of gravity ; if force be 

V . _., 3L3 applied vertically at E, no motion would be 

- — D produced ; but if force be applied at B, di- 

directly opposite the centre of gravity, it would be destroyed 

by the inertia of the mass, or if great enough to overcome 

this, would move the body before it. If a small degree of 

force were applied at C or at D, or at any other point above 

or below B, it v/ould cause the body to rock or vibrate, and a 

greater degree of force would overturn it. 

WLat point in a body must be supported to prevent its falling? What is the 
centre of weight? Is the centre of magnitude always at the same point as the 
centre of gravity ? Point of the greatest resistance. 



CENTRE OP GRAVITY. §5 

222. A vertical line drawn through the centre of gravity 
is called the line of direction. If the line of direction fall 
within the base of any body, it will stand, but if it do not 
fall within the base, the body will fall. 

Fig. 45. 223. Suppose a piece of wood, A B C D, 

vr--^—-'"-"^ standing upon one end, and the centre 

/ of its gravity to be E, so long as the 

_: y line of direction falls within the base, 

the body will be supported ; but by 

__ placing on the block of wood another 

._ti:___- ,--i^^^— -block, A B GH, the centre of gravity 

of the whole pile is now at L, and therefore as the line of 
direction, LD, falls without the base D, the centre of gravity 
is not supported, and the whole will fall. A carriage of any 
kind moves most securely over a level road,because the centre 
of gravity then falls exactly between the wheels, and is 
best supportedo Where one side of the road is much higher 
Fig. 46. than the other, there is always danger 

r that a carriage will be overturned, and 

this danger is great in proportion to 
the height of the carriage or of the load 
'\ which it contains. The figure repre- 

i[ sents a cart loaded with wool. Suppose 

^^^^. \^ A to be the centre of gravity, the line 
'^Sj'l,,.'^^^ of direction is then towards C, which 
J^^ not falling within the wheels, is not sup- 

C ported by them, of course the load must 

be upset. But supposing part of the load to be taken off, or 
that instead of wool, which is comparatively a light sub- 
stance, the cart were loaded with iron or stone, the centre of 
gravity would then be lower, as at B, and the line of direc- 
tion, B D, being thus within the wheels, the body would be 
supported. 

224. When a carriage inclines much to one side, owing 
to unevenness in the road, the passenger should lean to the 
opposite side in order to keep the centre of gravity suj)- 
ported. In sailing in boats, people should be very careful 
not to get too much weight on one side, and in case of any 
danger of upsetting, they should not rise, as this would ele- 

Line of diiectiou. Iinpoitauco of the line of direction falling within the Ijase. 
Carriage inclining to one side. Boat. 



86 



NATURAL PHILOSOPH 



vate the centre of gravity, and thus increase the danger, 
by bringing the Hne of direction witliout the bottom of the 
boat. 

225. The form of bodies is of great importance in giving 
them firmness of support, for while some cannot be moved 
without lifting the centre of gravity, others can be set in 
motion by the shghtest force. The broader the lase, and 
the nearer the line of direction to the centre of it, the more 

firmly does a body stand ; ivhile the narrower the base of a body 
and the nearer the line of direction to the side of it, the more 
easily it is overthrown. 

226. In the following figures, the two particulars, base 
and height, are -combined in a series of proportions. The 




place of the centre of gravity in each figure is marked by 
a dot, and the curved line proceeding from it, shows its 
path when the body is overturned. This curved line is a 
portion of a circle which has the edge or extremity of the 
base'(& in fig. A) as a centre, because the body turning 
must rest upon such extremity or corner as the centre of its 
motion : p shows the line of direction, or where a plummet 
line if suspended from the centre of gravity would fall. 
In fig. A the base is broad, and the centre of gravity low ; 
before the body can fall over, this centre must rise almost 
perpendicularly ; and the resistance to overturning it, is 
therefore nearly equal to the weight of the whole body. 

227. Figures B, C, and D, (Fig. 47,) show the lines in 
which the body must fall to be more and more inclined as 
their bases become narrower ; consequently the bodies are 
less firm in proportion. B represents a square house, C a tall, 
narrow house, and D a very high chimney. At fig. E, the 



Importance of the form of bodies in giving tliem firmness. Various forms 
of bodies in relation to base and heigljt. 



CENTRE OF GRAVITY. 




centre of gravity being over a base which is a mere point, 

the body is in a tottering position, and at the least degree of 

inchnation would fall. 

228. Spherical bodies are ea- 
sily rolled down an inclined plane 
because their base is but a point, 
and the smallest force is suf- 
ficient to remove the line of di- 
rection out of its base. In the 
figure we perceive that the body 

A, by its line of direction, will slide down the plane D E, 

while B and C will roll down the same. 

229. A ball or cylinder rolls downwards by the force of 
gravitation, because its centre of gravity is approaching the 
earth, and is continually advancing the centre of motion. 
The difficulty of rolling heavy bodies ip an ascent arises 
from the centre of gravity being behind that of motion, and 
continually tending to impede its progress. In moving a ball 
or cylinder directly forward over a plane surface, the centre 
of gravity is not lifted up ; but it moves in a line parallel to 
the surface over which it passes, and the centre of motion is 
directly beneath it. 

230. The centre of gravity in any body which is left 
free to assume its natural position, is such that a line 
drawn from this centre to the point where the body rests 



Fig. 49. 




will be the shortest that can be drawn 
from the centre to any part of its surface. 
Thus an egg, or any other oval body, 
would not stand in the position represent-^ 
ed in the figure, but would turn until the 
shorter line, A C, became perpendicular 
to the supporting surfiice instead of the 
The centre of gravity, lolien ladies are 



B 

longer line, A B. 

not supported, always seeks the lowest sitLiation. 



Why are spherical bodies easily moved ? Why is it diflicult to roll heavy 
bodies up an ascent? When bodies are left free, where will the centre of grav- 
Viy rest ? 



88 



NATURAL PHILOSOPHY. 




231. If a body be suspended from a fixed point, the cen- 
tre of gravity will always be in a vertical line beneath the 

point of suspension. Suppose the 
figure to represent a piece of board 
suspended from the point a ; let a 
plumb hne, ag, also be suspended from 
a, and mark the direction of the string 
on the surface of the board. Then 
suspend the board from any other 
point, as d, and also the plumb line 
from the same point, and mark its di- 
rection, the point c, where the two 
lines cross each other is the centre of 
gravity. 

232. A ball or cylinder may be made to roll up an inclined 
plane by its own weight. Let A B represent a cylinder of light 

wood, having its centre of gravi- 
ty at c, and placed on the inclin- 
ed plane CD; it is evident that as 
its line of direction from the cen. 
tre of gravity, lies out of its 
base, it would roll down ; but if 
at g a ball of lead be inserted into the cylinder, it will then 
roll upwards till the lead gets as near the surface of the 
plane as possible, and therefore when the cylinder is ascend- 
ing, the lead is descending. 

Fig. 52. 233. When an oval body, 

A, resting on a level surface, 
B C, is moved to either side, 
the centre of gravity must rise 
as in the pendulum of a clock ; 
it will then descend, and thus 
^ G the original force vWiich set it 

in motion, and the force of gra=/ity, will cause a vibration or 





A body suspended from a fixed point. Cylinder rolling upwards. Oval body 
eslinsf on a level surface. 



CENTRE OP GRAVITY. 



89 



rockiDg ; a child's rocking horse and a cradle are examples 



Fig. 53. 




of this. The rocking stones 
or Tors, of Cornwall, in Eng- 
land, which are huge masses 
of rock, thirty or forty feet 
high, with a rounded base rest- 
ing on a flat surface, are so 
nearly balanced that a man's 
strength is sufficient to put them 
in motion. There are many 
toys for children which show 
the effect of placing the cen- 
tre of gravity very low ; the 
figure of a horse, with only the 
hind feet supported on a pedes- 
tal, represents a toy in which 
the weight of the ball below the horse, by bringing down 
the centre of gravity, causes a vibratory motion when either 
the rider or horse is touched. 

234. It would appear wonderful to one unacquainted with 
the principles which we have endeavoured to illustrate, to 
•p- ^^ see a pail of water support- 

ed by a stick lying loosely 
upon a table. Let A B rep- 

A.// B resent a stick resting on the 

edge of a table ; if left to 
itself this would naturally 
fall, because its centre of 
gravity is beyond the table ; 
but the pail, C, being sus- 
pended by a string, s, from the stick, A B, instead of pulling it 
down, supports it by means of another stick, C B, which rests 
against a niche in the end of the stick, A B, and presses 
against the string at the point from which the pail is sus- 
pended. Now the stick, A B, cannot fall without lifting 
the weight of the pail or raising the centre of gravity. 
On the opposite side of the table at P, is a common tobac- 
co pipe, which may thus be made to sustain any weight 
which is not sufficient to destroy the cohejion of its parti- 




Centrc of gravity placed low. Ilkistratiou of the cllects of a low place for die 
centre of gravity. 

8* 



90 



NATURAL PHILOSOPHY. 




cles. An umbrella or walking cane, hanging on the edge 
of a table, is supported on a similar principle. 

235. A building may lean consider- 
ably from the perpendicular, but will 
not fall so long as the centre of gravity 
is supported, or a^ vertical line drawn 
from it falls within the base.'i Thus a 
column or steeple might, without en- 
dangering its stability, have an incli- 
nation still greater than that: in the 
figure where the line A B represents 
the line of direction, but this would not 
be the case in the annexed figure, where C D falls jvithout 
the base. 

236. Tall spires and turrets, after a lapse of time, are often 
seen to lean from the perpendicular, but if they are properly 
Fig. 56. constructed they may long endure even 

in this state. In Pisa in Italy, where are 
many ancient and remarkable buildings, 
is a celebrated leaning tower, which was 
built in the twelfth century. It is of mar- 
ble, 168 feet in height, and leans sixteen 
feet from the perpendicular. Some sup- 
pose that this beautiful tower was designed- 
ly built in this manner in order to escite 
emotions of wonder in the spectator ^who 
beholds its lofty top thus bewding over 
its base ; others believe it to have gradually sunk to its present 
position. 



Building le&ning from the perpendicular. Tower of Pisa. 



CENTRE OJi' GRAVITY. - Ql 

237. When two bodies of equal weight are connected 
by a rod, the centre of gravity will be in the middle of 
Fig. 57. the rod, and a string 



A 




fastened to this point 
will hold the whole in 
equilibrium. But if the 
bodies are of unequal 
weight, the centre of 
gravity is nearest the 
greater weight. That is, if a be a weight of three 
pounds, and b, a Vv'eight of one pound, the two will be bal- 
anced if suspended at a point in the rod c, three times nearer 
to the centre of the large weight, than to that of the small 
one. 

238. A. person can carry two pails of water with nearly 
as much ease as one, because the two pails balance each 
other, and the feet more naturally sustain the centre of gra- 
vity than v/hen this is thrown on one side by the weight of 
only one pail. 

239. The centre of gravity is also the centre of iner- 
tia. 

240. If a person lift a rod of uniform density by the 
middle, he overcomes the inertia of the whole mass. If he 
lift it by a part nearer to one end, the shortei', and conse- 
quently the lighter part will rise first, because the centre of 
inertia is in the other. 

241. The pupil will now perceive the intimate connection 
between the principles of natural philosophy and the me- 
chanic arts, since not even a chimney can be constructed 
without constant reference to the plumb line, as showing the 
line of its centre of gravity. The moderns, in their struc- 
tures, appear to study elegance and comfort rather than du- 
rability ; the walls of modern brick and stone buildings, 
being so slight that if they vary in the least from the 
perpendicular, they are in danger of falling, affording in 
this respect a great contrast to the massy piles of anti- 
quity. 

242. We have found that as the vast variety of motions may 



Centre of gravity in tvvo bodies connected. A person carrying- two pails of 
water. Centre of inertia. Inertia overcome. Mechanic arts connected with 
philosophy. 



92 NATURAL PHILOSOPHY. 

be all explained by a few simple principles, so by the single 
established fact of a centre. of gravity or inertia, we come 
to the conclusion that a force applied to this one point will 
produce an effect which cannot be produced by much great- 
er forces acting in different directions. 

243. The motions of animals, of 7nan particularly, illus- 
trate the laivs loith respect to the centre of gravity. We have 
found that a body with a narrow base, is less easily support- 
ed than one vvith a broad base, and that the greater height 
requires the greater base : but man walks erect, firmly sup- 
porting Install figure on a very narrow base, and in a vari- 
etyof attitudes. This supporting base is the space occupied 
by, and included between the feet. Persons who turn the toes 
outwards in walking, have then the advantage of a broader 
"base, which adds not only grace, but firmness to their 
gait. We may, in various attitudes of human beings, per- 
ceive these two qualities, grace and firmness, intimately 
connected ; by this we mean, that those positions in which 
the centre of gravity is best supported, are the most grace- 
ful. Thus if we contemplate the attitudes of a number of per- 
sons standing in a room together, we see some in postures 
which appear uneasy and constrained, and which occasion 
by sympathy a feeling of pain in us ; such attitudes are un- 
graceful, because it is the nature of grace to give pleasure 
to the beholder. We see others standing in attitudes which 
seem so easy, that we can scarcely conceive of their caus- 
ing fatigue if ever so long continued. The best rule for fine 
attitudes, is to keep the centre of gravity of the body well 
over the base. This centre in the human being is between 
the hips ; now by setting the feet in parallel lines, and 
close together, the figure looks as if it were not firmly sup- 
ported ; and as if considerable muscular effort were necessa- 
ry in order to keep the body erect. 

244. In sitting down, or in rising from a seat, much of 
the grace of motion depends on the manner in which the 
centre of gravity is lowered or raised. Some persons drop 
into a chair as if they were mere lumps of inert matter, 
influenced only by gravitation ; whereas the muscles of 
the lower limbs should 

Effect of force properly applied. Laws of gravity illustrated by the motions of 
animals. Attitudes. Rising and sitting down. 



CENTRE OP GRAVITY. 



93. 



centre of gravity may descend slowly and gracefully. In 
rising from a seat, the body must be inclined forward, in order 
to bring the centre of gravity over the feet or base, and in this 
position the muscular force of the hips and lower limbs is suffi- 
cient to effect the object. But feeble and aged persons, by ta- 
king hold of some firm support by their hands, assist the mus- 
cular efforts of otlier parts of the body. 

245. Dr. Arnott, a popular writer on Natural Philosophy, 
says that a man agreed to give ten guineas for the privilege 
of attempting to possess himself of a purse of twenty guineas, 
by picking it up when laid before him on the floor, but that he 
lost his money. The conditions were that the man should 
stand with his heels against a perpendicular wall, and in 
this position, by bending his body, should pick up the purse. 
Now under these circumstances, the forward inclination of 
his head and arms would throw the centre of gravity be- 
yond the base, and he must fall ; in order to reach the floor 
with his hands, it was necessary that he should have thrown 
one foot backward, which the wall prevented. 

246. In walking, the centre of gravity is alternately over 
the right and the left foot ; if one foot is injured so that it sus- 
tains the weight of the body with difficulty, the lame person 
is seen to advance only with the well foot, using the former 
merely to rest upon while the latter is doing the labour of mo= 
ving the weight. 

247. A person carrying a burden on his back leans for= 
ward ; if the weight be in his arms he leans backward, if on 

Fiff. 58. Fig. 59. 





his head, he walks erect. If the load be on one shoulder, he 
leans to the other side. When a person stumbles with one 
foot, he extends the opposite arm. In ascending a hill a person 
bends forward, and in descending he leans backward. In all 



Ascending and descending 



M NATURAL PHILOSOPHY. 

these cases the object is to support the centre of gravity, and to 
bring the centre of direction within the base, that is, the feet. 

248. The young child does not learn to stand, much less 
to walk, till long practice in position has taught him how to 
support his weight, and the muscular efforts necessary to 
move it. But the kitten, and other quadrupeds, sustained 
by their broad bases, have no need to learn the art of stand- 
ing. But we seldom see these animals raising the two feet 
on one side at the same time. 

249. The vegetable kingdom, no less than the animal, 
seems subjected to the great law of nature which we have been 
considering. Tall trees have their roots wide spreading, 
in proportion to their height, thus furnishing a broad and firm 
basis of support. Their line of direction also is as unerring 
as in any works of art ; the pine and fir grow as perpendic- 
ularly as the builder can construct a column. Who will say 
that a divine master builder does not rear these stately pil- 
lars of the forest, nature's temple? Upon the hill side as 
upon the level plain, with undeviating regularity they rise 
toward heaven as if to do homage to their Creator. When 
from any accidental cause, there appears a deviation from 
the ordinary direction of a plant, we always find a corres- 
ponding change in the basis which supports it. Thus, where 
the trunk leans from the perpendicular in one direction, the 
root spreads farther in the other ; as the man throws one 
foot behind him, when he leans forward. Having con- 
sidered the properties of matter, and the laws by which it is 
governed, we are prepared to consider the application ol 
these subjects to the various branches of Natural Philoso- 
phy. One of the most important of these branches is Me- 
chanics, the doctrine^ of which v/e have noticed under the 
heads of motion and gravity. We shall therefore next give 
our attention to the mechanical powers. Writers on Philos- 
ophy sometimes divide Mechanics into the two departments 



Centre of gravit}'^ in quadrupeds well supported. Centre of gravity in plants. 
Division of the subject of mechanics. 



CENTRE OP GRAVITY. 95 

of Statics,'^ or bodies at rest, and Dynamics,-\ oy bodies in mo- 
tion. But as the different states of bodies at rest, and bodies 
in motion, are the results of different modes of acting of the 
same cause, we have not thought proper to make this sep- 
aration. 

* From the Greek verb stasis, standing. 
From the Greek Dunamis, power, or force. 



PART II. 

OF THE MECHANICAL POWERS. 



LECTURE XL 

MACHINES. THE CORD. THE LEVER. 

250. Science would be of little use to man, were it not 
capable of practical application. The subjects which we 
have considered, as motion, force, and gravity, are indeed 
highly interesting as parts of a system of philosophy, and 
because they explain many of the phenomena of nature. 
But as we are not placed in this world merely to be amu- 
sed, that philosophy which had no higher object would be 
scarcely worth the name. Knowledge is valuable in pro- 
portion as it contributes to the comfort and happiness of man, 
or elevates and ennobles his soul. We have many wants, 
which can be supplied only by labour and industry ; such 
inventions therefore as tend to facilitate labour, and give ef- 
fect to industry, are of great value. We are indebted to 
science for most of those improvements in the arts and man- 
ufactures, vvhich give to the moderns such great advantages 
over the ancients, not only in supplying necessary wants, 
but in greatly increasing facilities for the acquisition of 
knowledge, and in adding to the enjoyments and luxuries of 
life. 

251. That department of Natural Philosophy called Me- 
chanics, exhibits the great principles by means of whose ap- 
plication machines are constructed, and operate ; these prin- 
ciples we have endeavoured to explain and illustrate, in the 
preceding chapters. The utility of machinery consists in 
the addition which it makes to the power under the controul 

Science valuable for its ]jractical ap[)lication. Science promotes the arts and 
manufactures. Adds to the enjoyments of life. Mechanics. 



MECHANICS. 97 

of man, in the economy of time, and the application to valua- 
ble purposes, of substances v/hich would otherwise be use- 
less. 

252. Man, besides human strength, and the strength of 
other animals, has at his command the powers of water, luind. 
and steam, with the force of springs and weights. Water 
acts by its weight, and the velocity which it acquires in fall- 
ing. Wind acts b}'' its volume or mass, and its velocity, 
Sfeam, which is the vapour of water produced by heat, has 
a tendency to expand itself, and its force is proportioned to 
the heat which generates it, and the pressure to which it is 
exposed. The strength of animals is commonly made to 
act upon some centre of inertia, by drawing, pushing, or 
pressing. 

253. There are three important circumstances to be con- 
sidered in machinery. 1st. The v/eight to be raised, or the 
resistance to be overcome. 2d. The power by which this 
is to be effected : and, 3d, The instruments employed. 

254. Motion is to he produced, and this motion must he 
properly applied. The instruments employed for communi- 
cating motion, are called by various names. A tool is the 
most simple instrument, and is generally used by the hand ; 
as a shoemaker's awl ; a carpenter's saw. A machine is a 
complex tool, or a collection of tools, and frequently put in 
action by inanimate force, as a carding machine, which is 
m.ovedby the force of running water; an engine is a pow- 
erful and complicated machine, as the steam engine. 

255. The ancients made little use of machines except in 
war, and in the erection of their stupendous works of archi- 
tecture ; and these machines were chiefly moved by the 
strength of men and animals. In building the Pyramids of 
Egypt, it is said that 100,000 men were employed for twenty 
years; it is estimated that by the aid of modern machinery, 
one man could pow in the same time perform the labour of 
27,000 of the Egyptian workmen- 



Utility of raacliineiy. Tiie forces under the controul of inan. How these 
forces operate. Circumstances to be considered in machinery. lustnimcnls em- 
ployed for communicating motion. Tool. Machine. Engine. Rlachines of 
tlie ancients. Advantages of modern rnachinerv. 

9 



98 NATURAL PHILOSOPHY. 

256. Machines were^rsi invented by men for the purpose 
of raising great weights, and overcoming great resistanceSc 
Tliey do not produce power or force, bat modify, its effects, 
that is, they increase or diminish the velocity of the moving 
power, change, its direction, and accumulate momentum in 
order to exert it at one single effort ; or they distribute force . 
among a great number of resistances, so dividing the force 
of resistance that it may be overcome by a series of actions, 
or by the continued action of the moving power. 

257. The term meclianical powers, has been improperly 
given to a ^qw simple machines, which are either used singly, 
or are variously combined to form complex machines. We 
say improperly given, because as already observed, these 
machines are not in reality powers, neither do they create 
power ; but aiding man so greatly in the adaptation of the 
powers of nature to his use, it was natural that he should be 
led to consider them as the prime agents, when in fact they 
are only secondary, and subservient to the existing powers 
of nature. The simple mechanical powers are, the Cord, 
the Lever, and the Inclined Plane. 

The Cord. 

258. If a man wished to transport any weight, a log of wood 
for example, without the assistance of the mechanical pow- 
ers, it is evident that he would take it up with his hands and 
carry it. In this case the force is applied merely to over- 
come gravity, and consequently acts in a vertical direction. 
Were a cord to be used to assist in transporting the log, the 
strength of the man in pulling would be exerted in nearly a 
horizontal direction. Thus the cord serves to change the 
direction of the force exerted by the man. The manner in 
which this force is modified is, that instead of overcoming the 
weight of the log, it only overcomes friction ; which though 
proportional to the weight of a body, is not equal to it, unless 
the body is subjected to pressure. 

The Lever. 

259. The Lever is a rod or lar, some point of ichicli being 

Macliines why invented. jManner of their operation. The efl'ect produced. 
Mechanical powers not prime agents. Names of the mechanical powers. Man- 
ner of their operation. The Lever. 



THE LEVER. 



99 



Fia-. 61. 




'Supported, the rod itself is movahle about that point,_ as a cen- 
tre of motion. The name lever was given, because this me- 
chanical power was first applied only to the raising of 
weights. 

260. The centre of motion is the fidcrum or prop. The 
force which gives motion is called the power ; that which 
receives it is called the weight. Suppose the figure to 

represent a weight about to 
be raised by a common crow 
bar, which is a lever ; a is 
the part of the lever at which 
the poiver or force is applied, 
f is the fulcrum, and b is 
the weight or resistance. — 

The lever changes the direction of forces into opposition ; 

that is, when the pouxr descends, the resistance ascends, viz. 

as the man's force presses dov^^n the lever, the weight rises. 

261. The beam or rod of a common balance is a lever 

with equal arn;is, the point 
by which it is supported is 
the fulcrum, and when the 
scales are empty, or con- 
tain equal weights, they 
are in equilibrium; be- 
cause the centre of gravi- 
ty, which is then in the 
middle of the rod, is sup- 
ported by the fulcrum f. 

If one scale contained a greater weight than the other, the 
centre of gravity would not be in the middle of the rod, but 
towards the greatest weight, which would descend, or out- 
weigh the weight in the other scale. 

262. Now if the fulcrum be removed, and placed nearer 
the greater weight, the scales would again balance each oth- 
er ; from whence it appears that the nearer the weight is to 
the fulcrum, the more its resistance is diminished. Thus if 



Fi?. 62. 



r 



Fulcrum, power, weight. Explain the figure. The common balance is a 
Jever. In what case the centre of gravity would not be in the middle of the lod. 
Effect of moving the fulcrum nearer to the weight. 




100 NATURAL PHILOSOPHY 

two balls, A weigh= 
j^ ^g- ■ • j^g three pounds, and 

B weighing but one 
pound, be fixed to the 
opposite ends of an 
iron bar, the bar would 
be in equilibrium, if 
suspended at the point c, three times as far from the lighter 
ball as from the heavier one. We may consider the bar as 
a lever, the large ball as the resistance, or force to be over- 
come, and the supporting point as the fulcrum. 

263. It is a fact well understood by children who amuse 

themselves by balancing upon a board, placed across some 

Pig. 64. prop, that when their 

weights are not equal, 

the board must be so pla- 

^^'lu^ . ; ced that the heaviest shall 

^ ;^t~«~-^ liW.^^***^^ i ^6 nearest the fulcrum. 




or centre of motion. Now 

the child at A moves 

B ^^^^pS^^^^^^^^^- ^ ^vith greater velocity than 
- -^f/e^^s^^^^j^^^^^^-r-::-^ Ij^g Qj^g ^^ g^^ because 

the former in rising and falling describes the arc of a larger 
circle, the two ends of the lever being the radii of two cir- 
cles ; and the longer the radius, (which is half the diameter,) 
the greater the circle. Thus if A C represent the part of 
the board, or arm of the lever of the lesser weight, this will 
be the radius of the larger circle, and B C, or the part of the 
board on which the greater weight moves, will be the radius 
of the smaller circle. Thus we see that by means of the 
lever, properly adjusted, the lighter child, whose strength 
alone would not be sufficient to lift the heavier one, actually 
balances him ; and were the latter a little nearer the fulcrum, 
the former would overcome the resistance of his weight, and 
cause his end of the board to ascend. When they are 
in equilibrium, the children cause the alternate rising and 
falling of the board, by means of pushing against the ground 
with their feet, which motion reacting, sends the board up- 



How may the bar connecting unequal weights be put in equihbriiim ? Great- 
est weight nearest the fulcrum. How may the hghter weight balance the heav- 
ier? 



THE LEVER. IQl 

ward, until gravity overcoming the momentum, it descends. 
You will perceive, that becausG tiie lighter child in rising and 
falling, describes in the same time the arc of a greater circle 
than the heavier child, the former moves with greater veloci- 
ty ; therefore velocity is here opposed to loeight, which is an 
important principle in mechanics. 

264. It will now be readily comprehended, that great 
weights may be raised with long armed levers, since the long- 
er the arm to which the power is applied, the greater is the 
effect produced by it ; because the velocity of the power is 
thus rendered proportionally greater than that of the weight. 
■In the example of the two children and the balancing 'board, 
the heavier child is to be considered the weighty or resistance, 
■and the lighter child the power. 



LECTURE XII. 

y THE LEVER. 



265. Levers are of three kinds, according to the position 
oj the power and weight with respect to the fulcrum. In the 
lirst kind, the fulcrum is between the power and weight ; 
in the second kind, the loeight is between the power and 
fulcrum ; in the third kind, the power is between the weight 
and fulcrum. 

Levers of the first kind. 

266. In a lever of the first kind, the fulcrum, F, is be- 
tween the 'power, P, and the resistance or weight, R. The 

^ Iig. 6o. examples we have heretofore given 

I 2S 1 ^^''® ^^^ °^ ^^^^^ \^mc\ ; but where the 

L^ DP g.^^^ fulcrum is equally distant from the 

>v^ two forces, as in the balance, there is 

no mechanical power, for as the two arms of the lever are 

equal, nothing is gained by velocity. False balances have 

Effect of velocity. The length of the lever should be proportioned to the 
weio-ht to be raised. Different kinds of levers. Lever cCthe firrt kind. 

9* 



^02 ' NATURAL PHILOSOPHY. 

the arms of the lever unequal. Thus a dishonest trader de- 
frauds both in buying and selling. In selling, he puts his 
o-oods in the scale, which is suspended to the longer arm, 
and here they appear to weigh more than they do in 
reality, by balancing a greater weight nearer the fulcrum. 
In buying, he would put the article of merchandize into the 
scale nearer the fulcrum, where more than the same weight 
would be required to balance the weight in the other scale. 
The fraud may be detected by making the weights and mer- 

_ ^ .^Mnmmnn,n.,.„„ '. chandlzc change places. A weight of one 

01 pound will balance another of iliree pounds, 
if the smaller weight be three times farther from the fulcrum 
than the larger one, (as seen in the cut.) 

267. If it be required to raise the stone, 5, (see the cut A,) 
which weighs 1000 pounds, by the strength of a man equal 

Fig. 66 




to 100 pounds weight, a lever, a c, which rests on the prop 
h, is placed with one end under the stone, and the man 
presses it down at the other end, a. As the man's strength 
is only equal to the tenth part of the weight of the stone, 
the arm of the lever, h a, must be ten times as long as the 
arm h c, in order that the power and weight may balance 
each other. B, fig. 65, is an illustration of the same prin- 
ciple. 

268. The steeLyard is a lever of the first kind, having 

Fig. 67. its arras unequal ; and any weight, as 

"^^ " t 4 5 € ^' ^^ ^^'® \ong arm, will balance as 

d ; ^ I ' ' ' I ' c'/' ' ' ^ miuch more weight than a, on the short 



•^ 3i arm, as b is farther from the fulcrum 

than a. Thus if the hook at the short 
end be one inch from the fulcrum/", a 
pound weight, J, will balance four pounds, a, at the short 
arm. If the article to be weighed be heavier than h, or 

False balances how contrived. To move a weightof 1000 pounds by a force of 
100 pounds. The steel-yard. How can a pound -weight balance four pounds? 



THE LEVER. 



103 



more than four pounds, it must be removed farther from the 
fulcrum in order to find its equipoise against the weight a ; 
if hghter than b, or less than four pounds, it must be nearer 
the fulcrum. The figures on the long arm of the steel yard 
represent pounds, the divisions between them half pounds. 
Steel-yards are usually marked into halves aad quarters, 
and sometimes contain sixteen notches, representing ounces. 
A steel-yard has usually two graduated sides, one tor small- 
er, the other for greater weights ; on the side for the 
greater weights, the fixed or standard weight is placed near^. 
er the fulcrum. 

269. A poker is a lever of the first kind, the grate upon 
Fig. 68. which it rests is the fulcrum, the coals 

the weight to be overcome, and the hand 
the power. A pair of scissors is com- 
posed of two levers acting contrary to 
each other, and held together by a rivet 
which is the fulcrum. In using them the 
hand is the power, and the article cut the 
resistance. The handles are usually nearest the fulcrum, 
and are then the short arms of the levers ; materials 
which are hard to cut, are best operated upon by putting 
them near the rivet or fulcrum. In shears used by tinners 
for clipping tin, the handles are very long, thus giving an 
increase of power by bringing the resistance near the ful» 
crum. Pincers and sugar cutters are double levers of the 
first kind, or in which the fulcrum is between tlie forces, 
that is, between the power and resistance. 

■pia. 69= 270. The fig. shows 

a long single lever 
turning on a strong 
iron pin as a fulcrum ; 
the long arm. gives a 
— "-^A great advantage in 
raising heavy bodies, as by means of it a small power acting 
at A, may overcome a great resistance at B. 

271. An ancient philosopher, Archimedes, said, "Give 
me a lever lon<T enough, and a fulcrum stroni^ enough, and 





If the 'Aeight be greater cr less tlian four pounds. Other examples of the 
lever. Advantage of a loiisr lever. Assertion of Archimedes. 



104 



NATURAL PHILOSOPHY. 



iwith my own weight I will lift the world ; " but as a power 
acting by a lever produces a force greater in proportion as 
its distance from the prop, or fulcrum, is greater because of 
:the greater velocity thus acquired, it follows from mathe- 
matical demonstration, by comparing the power with the 
resistance, that the philosopher must have moved with the 
velocity of a cannon ball for millions of years in order to 
jaise the earth the smallest part of en inch. This may be 
illustrated by a common example, that of prying a nail by 
jiieans of what is called a claw-hammer, which is a bent 
lever. Let the handle or shaft of the hammer be six 
times as long as the iron part that draws the nail, and which 
rests against the board, a man will pry up the nail with 
pne sixth part of the power that he must use to pull it out 
of the board with a pair of pincers ; in the latter case the 
nail would move as fast as the hand, but in the former the 
hand would move over six times as much space as the nail 
by the time the nail is drawn out, that is, the hand must move 
six inches in order to move the nail one inch. 



Levers of the second land. 

272. In a lever of the second hind, the 
weight is between the fulcrum and the 
power; in this case the two forces, that 
is, the weight and power, are on the same 
side ; the more distant force acts as the 
wLji pov.^er, the other as the weight or resist- 
ance. In the figure a hand-spike is represented as a lever 

Fiff. 71. 





of the second kind ; the ground being the fulcrum, the barrel 



Velocity necesssry to move the eai th Avilh a kver. Illustration. Lever df 
the second kind. 



THE LEVER. 105 

the weight to be moved is next, and the hand, which is ther 
power, at the end opposite the fulcrum. 

273. The advantage gained by this lever, as in that of 
the first kind, is great in proportion as the distance of the 
power from the fulcrum exceeds the distance of the weight 
from it. Thus if the point a, (in the preceding figure), at 
which the power acts, be-five times as far from c as the point 
h, on which the weight acts, then one pound applied to a will 
raise five pounds at b. 

274. Two persons carrying a burden upon a pole, bear 

shares of the load in 

Fig. 72. the inverse proper- 

B A tion of their distances 

from it ; that is, the 
one who is nearest 
bears the greater 
share ; if A be four 
times as near the load 
^^ as B, then A will bear 
^^ four times as much of 
the weight asB. 

275. Two horses of unequal strength may have the load 
to be drawn proportioned to this inequality, by dividing the 
beam they pull in such a manner that the point of traction 
or drawing may be proportional!}^ nearer to the stronger 
horse than to the weaker. 

276. A door moving on its hinges is a lever of this kind. 
The hinges are the fulcrum or centre of motion, the door is 
the weight or resistance, and the hand, in opening and shut- 
ting, is the pov/er. Let a person attempt to push open a 
large heavy door by usin,:^ liis strength near the hinges or 
fulcrum, and he v/ill find much force necessary, whereas by 
pushing at the [)iu't farthest from the hinges, he will move 
it with ease. If, while a person is sitting upon a bench near 
the middle, one should attempt to raise it by one end, the 
resistance v/ould be much greater than if the person were 
sitting at the opposite end. 



Advantngep'aiiied by Uiis lever. Example of a lever of the socoml Iciiul. Di 
viding the weiglit. Load made to bear upon the stronger horse. Door uiovinjj 
on its hinges. Raising a bench. 




106 NATURAL PHILOSOPHY. 

277. The oar of a boat, is also a lever of the second kind , 
the water being the fulcrum, the boat the resistance, and 
the hand of the rower the power. The mast of a ves- 
sel, may also serve as an example, the bottom of the vessel 
being the fulcrum, the vessel the weight, and the wind the 
moving power. 

Levers of the third kind. 

Fig- ''S-^ 278. In levers of the third kind, ihe 

^T/^ poller is applied between ih<i weight and 
C7 \^ ^^^^ fidcrum ; that is, the resistance is at 

'■■■"p ""1 one end, and the fulcrum at the other. 

y,^f\ No mechanical advantage is gained by 
this kind of lever ; for the power must always exceed the 
weight in the same proportion, as the distance of the weight 
from the fulcrum, exceeds the distance of the power. 

279. A ladder which is to be raised from a horizontal po- 
sition, and placed against the wall of a building, is first moy- 
jpjg 74. ed by the lower rounds, and is then a 

lever of the third kind, the upper por- 
tion of the ladder, being the resistance 
to be moved, the hand the power, and 
the ground the fulcrum. You v/ill perceive that here, the 
longer part of the ladder, or the resistance, has the advan- 
tage in velocity, which is possessed by the power acting at 
the long arm of a lever of the first kind. The nearer to the 
ground, or fulcrum of the ladder, the power of the hand is 
applied, the more difficulty is met with in raising the weight. 
The shears used for shearing sheep, are double levers of 
this kind ; the parts are not connected by a rivet, which 
forms the fulcrum in common shears, but the pov/er of the 
hand acts by pressure on a part near the middle, the ful- 
crum, or support, being at the end opposite to that in which 
is the resistance, or the wool to be sheared. The advantage 
of these shears is that little force is needed ; what the power 
loses, is gained in the velocity with which the parts next to 
the resistance act. In using the common fire tongs, the 
'ends of the tongs move v/ith much greater velocity than the 



Oar of a boat. Mast of a vessel. Lever of the third kind. A ladder raisee 
by the lower round, a lever of the third kind. Double levers. 




LEVERS. 107 

fingers, and it is only a small weight that we can lift with 
them, and this weight is less in proportion, as the legs of the 
tongs are long. 

280. The hones of animals are levers of the third kind, 
and are moved by muscles so situated, as to give rapidity of 
motion at the expense of power. Here the bone may be 
Fig* 75. considered the lever, the joint 

the fulcrum, and the muscles 
the power. In the human arm, 
the elbow d, is the centre of 
motion, or fulcrum ; at c, is the 
muscle, which acts as the pow- 
er in raising a weight, a ; the 
muscle being about one tenth part as far below the elbow 
as the hand, it follows that it must exert a power equal to 
one hundred pounds, to raise a weight of ten pounds. By 
this we see how strong must be the muscles, which give 
power to the animal frame ; but this strength seems neces- 
sary in the position they occupy, acting as they do, at the 
mechanical disadvantage of being so near the fulcrum. But 
by this loss of power, as we have seen, in examples of the 
third kind of levers, m.uch is gained in velocity, and to man, 
with all his advantages of various mechanical powers for in- 
creasing force, it is of great importance that his hands are 
so supported, that he can move them with quickness, and 
adapt them readily to a great variety of motions, impelling 
other forces at his will ; and causing them to obey his 
bidding. 



Fire tongs a lever of the third kind. Bones of animals how moved. Velo- 
city gained at the expense of power. 



108 



NATURAL PHILOSOPHY. 



L E C T U R E ' X 1 1 1 



THE I^XLIKED PLANE. 

2S1. The inclined plane is the most simple of the me- 

chanical powers. It is a plain or smooth surface, inclined 

towards the horizon, and is used in I'aising heavy weights. 

A plank placed in a slanting position, for the purpose of 

Fig. 76. roiling up casks into a warehouse is an ex- 

-^ ample, a c represents an inchned plane, 

" a b its height, and h c its base. That a 

weight could be more easily rolled up a slope, than raised 
perpendicularly is very evident ; but the advantage is gain- 
ed at the expense of time, because instead of moving directly 
from 1) to a, it moves over the .line a c, the resistance be- 
ing less in proportion, as the line <2 c is longer than the 
line a b ; therefore, as the length of the plane is to its height, 
so much is the resistance diminished. In the inchned plane 
the power has to overcome onl}^ a portion of gravity at a 
time, and this portion is greater or less as the plane is more 
or less elevated. On a plane perfectly horizontal, as at A, 
the pressure of a body is entirely sustained by it, or, the 
pressure on the plane is equal to the whole force of gravity. 

Fi?. 77. 



nii 





When one end of the plane is elevated, as at B, the force of 
gravity is resolved into tv/o forces, one acting parallel to the 
plane, and the other perpendicular to it. In proportion as 
the plane is more elevated, that part of the force of gravity 
which acts in a line with it is increased, and when the 
plane is raised perpendicularly as at C, the whole force of 
gravity acting in one direction, causes \he body to offer an 

Inclined plane. Advaniage gained at the exi:ense onime. Rulj. 



INCLINED PLANE. 109 

.-undivided resistance to the power which should attempt to 
support it. 

282. The 'power applied in raising a weight upon an in. 
.dined plane, must he to the weight, as the height of the plane 
is to its length. 

283. Suppose the perpendicular height A B, to be one 
foot, and tlie inehned surface, A C, to be four feet ; then a 

Fig. 78. weight of four pounds, W, rest- 

V7 A ing on the plane, will balance 

^^^^i:::^^^^-^^ one pound, P, acting over a pul- 

C J® ley ; that is, one fourth of the 

v/eight necessary to lift a weight through the space A B, or 
the vertical height, would be sufficient to force it up the in- 
clined plane from C to A. Thus it will be seen that what 
is gained by power is lost in time, which is the case with ail 
kinds of machines. From the simple nature of the inclined 
plane it is probable that it was used in remote periods of 
antiquity. The Egyptians are supposed to have made use 
■of very long inclined planes in elevating the huge masses 
of stone which form the pyramids. 

284. Roads over declivities are inclined planes. A horse 
in drawing a load over level ground meets with no resist- 
ance from gravity ; he drags but does not lift the weight, 
that is, the resistance is from friction, which being proportioned 
to weight, is of course greater with a heavy, than with a light 
load. But in drawing the load up a hill, the horse has, in 
addition, to overcome more or less of the force of gravity ; 
that is, he lifts a part of the load, and this part is greater in 
proportion to the steepness of the ascent ; or, in other words, 
he lifts such a part of the weight as bears to the whole 
weight, the proportion that the perpendicular height of the 
hill bears to its length. If in the length often feet there is 
a rise of one foot, the horse lifts a tenth of the load. Rail 
roads are constructed on the principle of the inclined plane. 
They are made either perfectly level, or with so gradual a 
slope, that the drawing horse, or steam engine, has little 
more than the friction of the carriage to overcome. By 
means of rail roads, the hills and valleys of an uneven coun- 
try are reduced to horizontal and inclined planes. Rail- 

Proportion betweon power and weii^'ht Example, What is gained ly power 
is lost in time. Inclined planes used by the Egyptians. Roads npon declivities. 
In drawing a load up a hill, what is to be overcoaio i" Rail roads, inclined planes. 

10 




110 NATURAL PHILOSOPHY. 

ways are sometimes so constructed that any weight, as a 
loaded sledge, may be made to ascend one plane or inclined 
rail road by the impulse of another carriage with which it 
is connected, and which at the same time descends an ad- 
joining rail road. 

285. Bodies descending freely doicn inclined planes, move 
iviih a uniformly accelerated velocity ; but this velocity is not 
so great, as in falling through an equal space in a perpendic- 
l^ig' ^9- ular direction. Thus supposing the 

distance from A to B, to be equal to 
that from A to C, the former an inclin- 
ed plane, the latter perpendicular ; a 
ball falling from A to C, would acquire 
greater velocity, than in rolling down 
D the inclined plane, to B, but let the ball 
move from A to D, at the base of the plane, and its velocity 
will be equal to that gained by falling from A to C ; thus, 
the velocity acquired in fatlnig from an inclined plane is 
equal to that acquired in falling through the perpendicular 
height of the same plane. 

Compound Mechanical Powers. 

286o The three mechanical powers which we have con- 
sidered, viz., the Cord, Lever, and Inclined Plane, appear 
under the different modifications, of the Wheel and Axle, 
the Pulley, the Wedge, and the Screw. The Wheel and 
Axle, is a variety of the Lever, both machines being regu- 
lated by the same principle. The Pulley depends for its 
utility upon the Cord, though as it is used with Wheels, it 
■partakes of the nature of the Lever. The Wedge is a 
double Inclined Plane, acting on the same principle as the 
Single Inclined Plane, but wiih twice the effect. The Screw^ 
which is a modification of the Inclined Plane, operates 
through the aid of the Lever. 

Having described the elementary parts of these machines, 
we will nov/ consider them in detail. 



Velocity of bodies .moving freely down an ii clined pleiie. Rule. DitFerent 
m jdifcations of the mechanical powers. 



I'HE PULLEY. Ill 



LECTURE XIV. 



THE PULLEY. 

287. The cord is the essential part of the pulley, but this 
cannot be used to advantage without a wheel. If a rope 
were perfectly flexible, it migl:it be bent over any sharp 
edge, and thus enable force to overcome I'esistance, or to 
communicate motion in any desired direction. 

238. Suppose P to be such an edge, with such a rope 
passing over it ; a sufficient force, F, acting in the direction 
Fig. 80. F P, would overcome the resistance R, and 
I produce motion in the line R P. But as no 
materials of which ropes are made can be per- 
fectly flexible, and as they are rigid in pro- 
portion to their strength, or ability to transmit 
|;r force, cords could not be applied to machiner}^, 
except some means had been devised to over- 
come these obstacles. If a cord were to be used to trans- 
mit a force from one direction to another, it would require 
some force to bend it over the angle P, and this by its sharp- 
ness, would soon break the cord. 

289. By bending a cord over the surface of a curve, it 
may be made to sustain a certain weight, but when motion 
is to be produced, the rope in passing over the curve would 
meet with much resistance from friction. But in the pulley 
the curved surface moves with the rope, and thus is obviated 
the difficulty which otherwise would attend the use of this 
mechanical power. 



Essential part of the pulley. Cord passing over an edge or angle. Curved 
surface of the jjulley. 





112 NATURAL PHILOSOPHY. 

290. The wheel of the pulley is called &■ 
sheave ; this is fixed in a Nock and turns 
upon a pivot. In the edge of the wheel is a 
groove made for the rope to move in, the 
wheel itself revolves on the pivot, which is 
its axis of motion. The figure represents 
v/hat is called Ql fixed pulley. 

291. The fixed pulley gives no mechanical advantage, 
but its chief use is to change the direction of forces. This, 
however, renders it of great importance, since in the appli- 
cation of power, whether of men or animals, there are al- 
ways some directions which are more convenient and ad- 
vantageous than others. A machine therefore, v/hich gives 
man the ability thus to transmit or change the direction of 
moving powers, is not less important than one which enables' 
him with the aid of a small pov/er to overcome a great 
weight. 

292. In raising a curtain, it would be very inconvenient, 
if a person were obliged to climb up, in order to roll the cur- 
tain to the height desired ; but by means of the pulley, the 
object is effected by the mere drawing down of a cord. So 
it is much easier to raise a bucket from a well, by means of 
drawing downwards upon a rope, fixed to a pulley, than to- 
lift the weight by pulling it upwards. Boxes, bales of goods, 
and casks, are thus raised to the upper lofts of stores, and 
huge masses of stone to thp fourth and fifth stories of build- 
ings. But it is in the rigging of ships, thai the pulley is 
chiefly used, as by its help in hoisting sails, and placing 
heavy anciiors, a smaller number of seamen than would 
otherwise be required^ are enabled to manage a ship. 



Wheel or sheave of the p'jlley. Use of the fixtd pulley. Applications of the 
pylley. 



THE PULLEY. 



113 




In order the better to adapt the power to the resist- 
ance, two pulleys are often used. 
The strength of a horse may be 
so directed as to carry heavy loads 
to great perpendicular heights. Thus 
suppose B and C two fixed pulleys, 
and A, a block of marble fastened to 
one end of a rope, while the other end 
of the rope, after being carried over 
the pulley B, passes round C, and in the 
horizontal direction thus given is drawn 
by the horse to which it is fastened. 
Every step of the animal causes an 
ascent of the stone, until arriving at the pulley B, it is ap- 
plied to its destined use by the workmen at the top of the 
building. 
Fig. 8 3. 294. By means of the fixed pulley fastened near 
the windov/ of an upper story, a man might let him- 
self down, to escape from fire, when other means 
were wanting.. If to one end of the rope were 
fastened a basket or chair, a person placed in it, 
and holding with his hands the other end of the 
rope, might let himself down, by gradually yield- 
ing the ropo. In the same manner a person might 
draw himself up from a well or mine. But at- 
tempts of this kind must be dangerous, except in 
the case of those whose muscular strength is great 
in proportion to their weight. 
295. Since the power and weight in a fixed pulley, when 
equal, balance each other, it is evident, that by its use, there is 
no increase of power. It will be seen by the 
figure, that if P, the power, and W, the weight, 
be of equal force, they will equally bear upon 
that portion of the cord which is between them 
and the wheel, and will then rest in equi- 
librium. Therefore, in order to produce mo- 
tion, the power P, must be greater than tlie 
weight. Neither is theie any thing gained 'in 
^ velocity, for the weight or resistance moves as 





Double pulley. ^ 

Power and weight in 



the pulley. 



Descent by means of the fixed pulley. Ascent by means of 
a fixed pullc}'^ balance each other when equal. 



10* 




114 NATURAL PHILOSOPHY. 

fast as the power ; that is, in pulling P down one inch, W is 
lifted up but one inch ; therefore with the fixed pulley a 
man cannot raise a heavier weight than he could by his own . 
natural- strength. 

296. The movable pulley gives to the power a double ad- 
vantage over the loeight. B represents a movable pulley in 
connexion with a fixed pulley C. The weight, W, is at- 

Fig. 85. tached to the movable pulley, and as it bears 
equally upon the t^vo parts of the rope which pass 
round the pulley B, the power P having only to 
resist the force B C, has to sustain but half the 
weight in order to balance W. Therefore when 
the power is equal to half the iveight, an equilibrhmi 
is maintained. If the weight is twelve pounds, it 
iWvvill be balanced by a power equal to six pounds ; 
but for every inch that the weight is raised, the rope must be 
drawn at P two inches, because each of the two folds of rope 
must be shortened one inch. With the movable pulley a 
man raises twelve pounds with the exertion of only so much 
strength as would otherwise be required to raise six pounds ; 
but in order to do this, his hands move through a space of 
two feet, when if he lifted the whole weight, they would 
only move through a space of one foot. Thus the advan- 
tage gained is in proportion to the space passed through. It 
is as if the weight were divided into two equal parts, and 
raised successively. The pupil will perceive that in the 
movable pulley, as in the lever, the deficiency in the 
power is compensated by greater velocity. 

297. Compound pulleys are combinations of many pul- 
leys, in which the weight is distributed over a greater num. 
ber of parts of the rope, each part consequently sustains a 
smaller portion of the weight. As the hands move over 
twice the space for every pulley, it follows that two 
acting pulleys increase the power four times, three acting 
pulleys, six times, &lc. 

Double advantage of the movable pulley. Cause of this advantage. Com- 
pound pulleys. Rule. 



TH3 PXLLEY. 



Fig. 87. 




'^ 



115 



298. The figure, (seei5^, repre- 
sents a system or block of pulleys, 
sometimes called a tackle. The rope 
is successively passed over the pulleys . 
above and below, until after passing 
over the fixed pulley, A, it is attached 
to the power. The weight is as many 
times greater than the power, as the 
number of the folds of cord. Fig. 87 
represents a tackle having the pulleys 
arranged side by side, in blocks placed 
one above another. In the upper block 
there is an additional wheel or pul- 
ley which adds one to the power of the 
machine. By means o^ four mova- 
ble pulleys, a weight of seventy-two 
pounds may be held in equilibrium by a power of nine 
pounds, because each pulley having two folds of cord, each 
of which is equivalent to one part of the weight, v/e divide 72 
by 8, and the quotient is 9. But the power when in motion 
will pass over eight times as much space as the weight ; 
therefore lokat is gained in poiver is lost in time. 

299. Owing to the friction of the wheels and blocks, and 
the stiffness of ropes, all the advantage which m theory is 
stated to be gained fj'om the use of blocks of pulleys is not 
realized ; it is estimated that nearly two-thirds of the power 
is diminished by these causes. The weight of the several 
parts in the machinery is also to be considered in estimating 
the advantage of this mechanical power. 



Rule. How may a weight of 72 pounds be held in equilibrium by a power 
of 9 pounds'? Effects of friction and of the stiffness of ropes. 



116 



NATURAL PHILOSOPHY. 



LECTURE XV. 




THE WHEEL AND AXLE. THE WEDGE. THE SCEEW. 

300. The wheel and axis is a v.heel turning round, to- 
gather with its axis ; the power is applied to the circumfer- 
ence of the wheel, and the weight to that 
of the axis by means of cords. Let 
AB represent an axle, which turns upon 
pivots at its extremities. Round this axle 
is coiled a rope, w-hich sustains the weight 
VV. A wheel, C, which is fixed to the axle, 
has coiled round it in the contrj^ry direc- 
tion, a rope from which is suspended the 
power P. In turning together, the wheel 
would take up or throw as much more rope than the axle, as 
its circumference or diameter is greater than that of the 
axle. If the proportions were as six to one, one pound at 
P would balance six pounds at W. 

Fig. 89. 301. The v.heel and axle is considered as a 

lever of the first kind, in which C, the centre 
^of the axle, represents the fulcrum, and acb, a 
.horizontal lever, with the weight W, and the 
power P, at the opposite ends. The radius of 
the wheel acts as the longer arm of the lever, 
and the radius of the axle as the shorter arm. 
f^ L i Therefore there is an equilibrium ichen the 
CI "w pou-er hears the same proportion to the weight 
as the radius of the axle c o, bears to the radius of the wheel 
no. Thus if the diameter of the wheel is ten times that of 
the axle, a power of one pound will balance a weight often 
pounds. 

302. Since the wheel and axle are shown to be of the 
same nature as the lever, the inquiry may naturally arise, 
" wherein consists the advantage of the former over the lat- 
ter ?" When a lever is used for raising a weight, it can act 




How is tlie power' apr. lied to the wheel and axle? Describe the operation of 
the wheel and axle. Wheel and axle conside: ed as a lever. Rule. 



WHEEL AND AXLE'. 



ivr 



Dut through a small space at a time ; but from its simplicity 
the lever is of grefit use in raising great weights through a 
short space. When a continuous motion is to be produced, 
as in drawing water from a well, raising ore from a 
mme, &c. some contrivance is necessary to render the ac- 
tion of the lever continuous ; the spokes or radii of the wheel 
and axle, acting as so many levers, and revolving regularly, 
and without intermission, produce this desired effect. 
■ 303. Although the axle is usually nothing but a cylinder 
fixed upon pivots, yet as it revolves about these as a centre 
of motion, it is in effect a wheel, and half its diameter, or 
one of its radii, bears the same proportion to the whole cir- 
cumference of the axle, as the spoke of a wheel to the cir- 
cumference of the wheel. 

Pig. 90. 304. In the common windlass used in 

'^^C drawing water, what is called the cranh 

or winch, B C, serves the same purpose 
A as a wheel, B C being the radius or half 
the circumference ; D is the handle by 
which the power is applied. At each 
_, revolution of the crank a circle is de= 
"1 scribed, and the effect of the revolution 
upon the axle is the same as if the wheel were entire. 
Therefore it follows, that as B C represents the spoke of a 
wheel, or the radius of a circle, the power will be increased 
in proportion as the circle described by B C is larger than 
the circumference of the axleB A. 

305. The capstan used in ships and in dock-yards for 
Fio-. 91. weighing heavy anchors or drawing 

vessels into harbour, is one of the 
most useful applications of the wheel 
and axle. In this the axle is verti- 
cal ; its circumference near the top 
is pierced with holes, into which, 
when the machine is to be worked, 
are inserted long levers called cap- 
stan bars. These answer the same 
purpose as th6 spokes of a wheel or the crank of a wind- 
lass. The men who work the capstan" walk around the 





Advantage of the wheel and axle coinj)ai-ed with that of the levt 
Vi^'indlass. 



j\x\>\ 



ns 



NATURAL PHILOSOPHY. 



ax]e, pressing the bars ibrward, and the cable is thus wound 
about the axle with a force sufficient to lift a heavy anchor, 
or draw a large ship into harbour. 

Fig. 92. 

306. The tread. mill is turn- 
ed by the weight of men who 
step forward as fast as the 
wheel descends, thus maintain- 
ing their horizontal position at 
the circumference of the wheel. 

iL ir ^^ 

307. Horses ma}^ be made to work a mill by being bar- 
nessed to the extremities of shafts or long levers fixed to an 
axle which they turn by walking in a circle, as in cider 
mills, brick yards, &c. The horse- boats used in crossing 
ferries are moved by the stepping of the animal upon a hor- 
izontal wheel. 

308. Cranes lor raising weights consist of an axle to 
wind up the rope which sustains the weight, and a large 
wheel at the circumference of which the power is applied.^ 
The figure represents a machine of this kind, in which an 

Flff. 93. 





animal moving within the wheel causes its revolution, and 
this, by winding the rope around an axle, raises the vreight. 
It will readily be perceived, from the great circumference of 
the wheel compared with that of the axle, that the increase 
of power in this machine must be great. 



Tread mill. M'lls and boats moved bv horses. Crane, 
increase of bower. 



;of its eret*. 



WHEEL AND AXLE. 



119 




Compound W heel and Axle. 

309. In the compound wheel and axle, the power is to the 
lueicfhi as the product of the diameters of all the smaller 
wheels, is to the product oj the diameters of all the larger 
wheels. 

310. Thus the power behig applied to the winch P Q., 
acts upon the small wheel A, which acts upon the large 

Pijj 94. wheel B, this upon C, and this again 

upon D, which exerts its original and 
accumulated power upon the axle E, 
which sustains the weight W. Now, 
if the diameters of the three smaller 
wheels, including that of the axle, be 
severally one fourth, those of the lar- 
ger wheels (of which the diameter of 
the wheel described by the winch PQ, 
that is twice PQ, must be considered as 
one) then the power will be to the 
weight as 1 X 1 X 1 ,: 4X4X4, that is as 1 to 64 ; and a force 
of ten pounds applied at P, will balance a weight of 640 
pounds applied at W ; or in other words, if one pound will 
balance 64 pounds, ten pounds will balance 640. 

311. " It is sometimes desirable to make a variable power 
produce a constant force. This may be done by 7nakingits 

Fig. 95. velocitij increase as its intensity 

^ Hg diminishes. We have an ex- 

'ample of this in the reciproral 
action between the main spring 
m mmmjsmmu^ i i ^m mm and fusee of a watch. The 
maui spnijg is coiled up m ilie box A, and is connected with 
the fusee B, by a chain. When the watch is first wound 
up, the spring acts with its greatest intensity, but then as the 
wheel B turns, it uncoils with the least velocity ; but on ac- 
count of the varying diameters of the wheels of the fusee, 
the velocity is continually increased as the intensity of the 
spring is diminished.'"* 

* 01in5trd"s Compeodinm. 




Relations of the power and weight in the compound wheel and axle. Rule to 
be applied to the action of the compound Avheel and axle. Constant force pro- 
duced by a variable powei-. 



120 



NATURAL PHILOSOPHY. 



mg-lat^ie and the 

Fi^. 96. 

I 



312. One turn of the axle on which the watch key acts, 
is, by the train of wheels attained to it, rendered equivalent 
to about four hundred beats of the balance wheel, and thus 
the exertion, during a hw seconds, of the hand, in winding 
up a v/atch, produces motion for twenty-four hours or more. 

313. Wheels may be connected by' bands, as in the turn- 
common spinning-wheel. A spinning- 
wheel, as A c, of thirty inches in cir- 
cumference, turns by its band a spindle 
of half an inch, h, sixty times for every 
turn of itself. If the wheels connected 
by bands are required to revolve in the 
same direction, the bands are arranged 

_ as in fig. A ; but if they are required to 
revolve in diffeTent directions, they are arranged as in fig. B, 
where the band is crossed. In spinning, where the twist of 
the thread is all one way, the band of the wheel is fixed as 
at A ; but in twisting two or more threads together, where 
the twist is in opposite directions, the band of the wheel is 
fixed as at B. Two persons, in twisting a string, stand op- 
posite to each other, and therefore ihe same motion of the 
fingers in each, produces a twist like that with the cross= 
banded wheel. 




The Wedge. 

314. The wedge may he considered as two inclined planes-^, 
whose bases are jomed. It is forced in between resistances, 
to separate them, instead of having the resistance moved 
Fig. 97. over its surface as in the inclined 

plane. The more acute the angle 
^^^^^^^A, at the extremit}- of the wedge, 
) the greater its power is estimated to 
be. But the wedge is used in such 
a manner that it is difficult to compute its actual power, as 
this must depend greatly ca the strength of the blow with 
which it is forced against a resistance. 



Effect of winding up h ^vatch. Wheels connected by. bands. Cross band. 
Wedee, and m uiaer o'' itsHiee described. Two circumstances upon wiiicJi its 
co\vei depends. 




THE SCREW. 121 

315. In splitting logs of wood, and masses of stone, this 
mechanical power possesses a peculiar advantage, as by its 
means a great force can be exerted through a small space. 

316. A wedge is of that form known in geometry, as a 
triangular prism. Suppose the edge or angle E F, impelled 

against a block of wood, by a force applied at 
the-surface A B D C, if the force be estimated 
'by Its weight, its effect will be in the ratio of 
the line D F, to the line G D, or, as the sides 
of the wedge to half its breadth. That is, the 
power is increased, either by diminishing the 
back of the wedge, or increasing its length. 
Sharp edged, and sharp pointed instruments, act on the same 
principle, as the wedge ; as the axe and chisel, knife, pin 
and needle, and the shoe-maker's awl. The angle of the 
wedge is rendered more or less acute, according to the pur- 
pose for which it is to be applied. In determining this, two 
things are to be considered ; the mechanical power, which 
is increased by diminishing the angle of the wedge, and the 
strength of the tool, which is also diminished by the same 
cause. There is therefore, a limit beyond which the sharp- 
ness of the instrument would destroy the requisite strength. 

317. Tools which act by pressure, may be made more 
acute than those which act by the force of a blow, and the 
softer and more yielding the substance to be penetrated, the 
less is the power required to act upon it, and the more acute 
the wedge may be made- Thus a cambric needle, and 
lancet, are manufactured in reference to the materials they 
are designed to work upon. An axe, for cutting wood, is 
more acute than a wedge for splitting iron. 

The Screw. 

318. The screw is an inchned plane, grooved spirally 
round a solid cylinder. A road ascending the side of a hill, 
or a high mound, is considered an inclined plane ; but, (^ 
instead of directly ascending towards the top of a hill, the 
the road should wind around it, it will not essentially 



Advantage of the wedge. Instruments which act on the principle of tlie 
wedge. Tools which act by pressure, more acute than those driven by a blow. 
Examples, Screw. Like the inclined plane. 

11 



122 



NATURAL PHILOSOPHY. 



A 



differ from the inclined plane ; such a road bears a strong 
resemblance to a screw. The screw has also been called a 
winding icedge, because it bears the same relation to a 
Fig. £9. straight wedge, that a road winding up a 

hill, bears to a straight road up the same 
hill. Let A B, represent a common round 
ruler, having a paper wound about it, cut 
in the form of an inclined plane, the edge of 
the paper being marked by a black line : 
D let the edge E C D, be applied to the ruler, 
and the paper rolled round it ; the ruler will then present 
the appearance of a screv/, the black line E C D, represent- 
ing what is called the thread of the screw. 

319. The advantage gained by the screw, depends upon 
the slowness of the ascent, that is, upon the number of turns, 
or threads in a given distance. 

320. The screw is generally used with a lever which as- 
sists in turning it ; and with this addition it is a machine of 
great force, either in compressing bodies, or in raising great 
weights. It is to this mechanical power that we are indebt- 
ed for the common printing press, and for most of the 
presses which are used in the arts and manufactures. 

321. In the figure, L represents the lever, this is attached 
to a part called the nut, which is a hollow screw, through 

which the screw S, passes. Within the 
nut is a spiral groove,made to fit the spiral 
thread of the screw. The nut,in ascending 
or descending the screw, (which we have 
shewn to be of the nature of the inclined 
1, plane,) travels in a spiral line, and the 
^ closer the threads of the screw, the great- 
er the power of the instrument ; though as 
it then requires more time to traverse it? 
we find that here, as in the other me- 
chanical powers, what is gained in power, is lost in time. 

322. The power of the screw is also affected, by the 
length of the lever which turns it ; for the greater the cir- 
cumference which the lever would describe in one revolu- 




Advantage of the screw. Lever used Avith the screw. Examples. The 
closer the threads of the screw, the greater the power. The leogtli of the lever 
alFects the power of the screw. 



FRICTION. 123 

tlon, the more powerful would be the action of the screw. 
In other words, the effect of the screw, is to be estimated 
hy the proportion between the space described by the jjozoer 
in one revolution of the screw, and the space between any 
tioo of its contiguous threads. Thus if the threads of the screw, 
a a, (fig. 100.) be as much as half an inch apart, and it be 
turned by means' of the lever L, extending three feet from the 
c^ntre of the screw, the advantage of such a machine will 
be as the number o^ half inches in the space described by 
the extremity of the lever, are to unity or 1. Nov*^ reckon- 
ing the circumference of a circle to be three times its diam- 
'eter, the circumference described with a radius of three 
feet (because there are thirty-six inches in three feet) will 
be 36 X 2* = 72 X 3 = 216 inches, and twice that number, 
or 432 to 1, will be the measure of advantage afforded the 
machine. 



LECTURE XVL 



FRICTION. MOVING POY/ERS. GENERAL REMARKS UPON 
MACHINERY. 

323. Friction is that resistance to a moving body, which 
is caused by inequalities of surface. No substance is per- 
fectly smooth ; surfaces which appear so to the naked eye., 
as polished steel or glass, are found, when examined with a 
microscope, to be rough and uneven like the face of a file. 
Thus when substances move in contact, the prominences of 
one passing into the depressions of the other, occasion more 
or less resistance to motion. 

324. Friction loears upon the surface of bodies that are 

* The radius is Aa/f the diameter of a circle; therefore 36 multiplied by 2 
makes the whole diameter 72 inches; — this being multiplied by 3, shows the cir- 
cumference to be 21(5 inches. 

Friction described. Machinery injured by friction. 



124 NATURAL PHILOSOPHY. 

constantly in motion, and thus in process of time renders the 
various parts of machines unfit for use. 

325. Cohesive attraction between substances in contact, is 
another impediment to motion, though not equal to that 
caused by the ordinary inequalities of surface. 

326. Friction is diminished by making smooth the sur- 
faces which are to come in contact ; but this must be done 
within certain limits, for great smoothness brings the bodies 
into such close contact as to produce a considerable degree 
of cohesion. 

327. Less friction is produced when the substances which 
rub against each other are of different kinds, than when of 
the same kind ; thus copper slides over brass more easily 
than over copper. Axles of steel are thus made to revolve 
on brass ; and in watches, the steel axles are often made to 
play in diamond or some very hard mineral. The skater, 
with his steel skates, moves more rapidly over ice, than he 
could move over polished steel. 

328. By covering the rubbing surface with oil, tar, or 
soap, the friction is diminished. The axles of carriage 
wheels, and of spinning wheels, and machines of all kinds, 
require the frequent application of these lubricating sub- 
stances, 

329. The friction between rolling bodies is much less, 
than between those that drag ; in certain kinds of wheel- 
work the axle is made to revolve on small wheels called 
friction rollers. Sleighs are made to move on runners of 

wood, with the bottoms covered with steel, as this slides over 
the snow path with little friction. In descending steep hills, 
it is common for the drivers of carriages to lock the wheels, 
or fasten them in such a manner, that the rolling motion is 
changed to the dragging motion. Thus by increasing fric- 
tion, the velocity of the descent is impeded. 

330. Friction is found to be proportioned to the quantity 
of matter in a moving body, and not to the extent of surface. 
Thus a brick which has a broad and a narrow side, is found 
to meet with equal resistance from friction, when laid on 
either side. If the pressure be increased by laying weights 

Cohesive attraction impedes molion. How friction may be diminished. Fric- 
tion less when the substances are of different kinds, than when of the same kind. 
Examples. Oil, &c., used to diminish friction. Friction between rolhng bodies. 
Friction rollers. Increase of friction impedes velocity. Friction proportioned 
to the quantity of matter. 



FRICTION. 



125 




upon it, the amount of friction will also be increased, and in 
an equal proportion. 

381. The degree of friction in moving bodies, may be as- 
certained as follows ; suppose a box, B E, to be laid upon a 
Fig. 101. table, T T. Let a silken cord, fas- 

"^ '^ 33 tened to the bottom of the box, be 
carried over the table and pulley at 
P, the scale, D, being suspended by 
the cord. If no resistance were of- 
fered to motion, it is evident that the 
smallest weight, attached to the cord, 
would draw the box tov/ards P. 
But the friction which always exists, prevents a small 
weight from drawing the box at all. But let weights be put 
into the scale D, until a sufficient force is obtained to over- 
come the friction, without giving the box an accelerated 
motion ; such a weight is equivalent to the amount of 
friction. 

332. Now let the weight of the box, (vvhichis supposed to 
have been previously ascertained) be doubled by placing in 
it additional weights, the pressure will be doubled, and it 
will be found that the weight of the scale D, and its load, 
which was before able to overcome the friction, is now in- 
adequate to this effect. Let additional weights be placed 
in the scale until the friction is counteracted as before, and 
it will be found that the v/hole w^eight necessary for this is 
exactly twice the weight which produced it in the former 
case. Thus it appears that a double amount of pressure 
produces a double amount of friction. 

333. When a heavy body is placed on an inclined plane, 
it will have a tendencjr to slide ; and will therefore remain 
at rest on such a plane, only when the retarding cause of 
friction is greater than the tendency for motion caused by 
the inclination of the plane. The angle of inclination, at 
which motion on an inclined plane commences, is called the 
angle of friction ; and sometimes the angle of repose. 

334. Friction may be considered a passive force. Its ef- 
fects on machines in a state of equilibrium are very different 



Illustration. Further illustration. A heavy body on an inclined plane. Its 
tendency. The angle of friction. Tlie effect of friction on machines at rest — 
and in motion. 

11* 



Igfe NATURAL PHILOSOPHY. 

from the effebts of the same force en Jonachines in motion. 
In the one case, friction assists the poicsr, in the other case, 
\\opjposes \U Thus a weight placed on an inchned plane 
will require a less power to support it. in consequence of the 
friction of the two substances ; and a weight suspended by 
a rope passing over a pulley, will require a less weight to 
balance it, on account of the friction of the axle. But the 
case is reversed when a machine is to be put in motion ; 
for then, friction makes a still greater power necessary, 
than would overcome the weight itself 

335. In calculating upon the effective force of moving 
powers, as applied to machinery, it is always necessary to 
make deductions, not only for the resistance arising from 
friction, but for the stiffness of cordage, and the imper- 
fections of the materials of which the machines are con- 
structed. 

336. The amount of fiction varies in the several raechani- 
cal powers. In the lever it is very little. In the wheel 
and axle, the friction of the wheel is in proportion to the 
weight, velocity, and diameter of the axle; the smaller the 
diameter of the axle, the less will be the friction. In the 
pulle}^, wedge, and screw, the friction is great. 

Advantages from Friction, 

337. Notwithstanding the inconveniences of friction, in 
retarding the motions of machinery, it is one of those pro- 
perties of matter which are of great utility. If all bodies 
were destitute of friction, it would be very difficult for us to 
grasp, or retain in oe.r hands, any solid substance. A knife, 
a pen, or a book, couid not be held without such an exer^ 
tion of muscular power as would be fatiguing. Without 
friction, it would be still more difficult to use our feet than 
our hands ; the pavement, or ground, would be more slip- 
pery than ice ; and our shoes offering no resistance by 
friction, we should find it difficult to stand still, and much 
more so to walk. 

Friction offers an advantage in rubbing, scouring, ^polish- 
ing, and grindirig. 



Deductions from force for friction and other causes. Friction varies in tLe 
differ ont mechanical powers- Utility of friction. Examples. 



MOVING POWERS. 127' 



Other Mechanical Powers. 

338. Besides the mechanical powers which we have enu- 
merated, there are other means of varying ,and accumula- 
ting force, which were it not for custom, might with equal 
propriety be considered as mechanical powers. Of these, 
Ere hammers, threshing flails, clubs, slings, &c., which ena- 
ble a continued moderate effort to overcome a great resistance. 

Moving Powers. 

339. In considering the subject of liquids, and aeriform 
bodies, we shall find some of the most effective powers for 
moving machinery. The mechanical pov/ers are of inesti- 
mable advantage to man, in enabling him to accommodate 
the various forces of nature, to the work which he has to 
perform. Thus he makes the running stream, thg water= 
fall, the wind, and steam, turn his mills, impel his vessels, 
and even carry him over the, ground, whither he would go. 
The heavy mill-stone is turned, and the most delicate fibres 
of cotton and silk are twisted, by these inanimate agents, 
which man has pressed into his service. ■ 

340. Gravitation, or weight, affords the nieans of origina- 
ting motion for many important purposes.. By the proper 
application of this power, is maintained the regular motion 
of wheel work, as in a common clock, where the downward 
pressure of the weights keeps the machinery in motion. 

341. Elasticity gives force to various mechanical agents. 
Elastic metals, such as steel, manufactured into springs, form 
the moving power in watches and various other kinds of 
machinery. 

342. Heat, from its tendency to expand bodies, may be 
, ranked among the moving powers. 

343. The application of the natural strength of man, must 
have preceded the employment of all other moving powers ; 
but the force of brute animals was, by man, early made sub- 
servient to his convenience. Oxen and horses appear to 



Other means of varving (ivid accamulating force. Examples. Liquids and 
aeriform bodies are moving- foi-ces. Examples. Motion is obtained by gravita- 
tion. Elasticity gives motion. Heat. The strength of man and brute animals. 



128 NATURAL PHILOSOPHY. 

have been employed in the labours of the field, in the most 
remote periods of antiquity ; and the ass, camel, and ele- 
phant, are mentioned in the Scriptures and other ancient 
records, as beasts of burd-en. 

344. The mechanical effects produced by the muscular 
exertions of living beings cannot be estimated with the 
same precision as those of other moving powers, such as 
steam, water, gravitation, &;c. The force of human exer- 
tion differs according to the manner in which it is applied. 
It has been estimated by some ingenious experiments, that 
the labour of a man employed in working a pump, turning 
a crank, ringing a bell, and rowing a boat, might be estima- 
ted respectively by the numbers 100, 167, 227, and 248. 
From this it appears, that in working a pump, the man la- 
bours to the least advantage, and that rowing a boat is the 
most advantageous mode of applying human strength. 

345. The labour of a horse, in a day, is reckoned equal 
•tQ that of five men. The strength of the elephant is com- 
puted to be equivalent to that of six horses. He will carry 
with ease 3000 or 4000 pounds, and move at the rate of a 
slow trotting horse, travelling with ease 40 or 50 miles in a 
day. The elephant was used among the ancients in war, and 
is now employed as a beast of burden in India, and other 
eastern countries. The camel is a most serviceable beast 
of burden, especially in the sandy deserts of Arabia, where 
for eight or nine days in succession this animal travels at 
the rate of SO miles a day without water, and v/ith little 
food, carrying 10 or 12 hundred weight. The dromedaiy 
is a sm.aller species of camel ; it is m.ore fleet, but less able 
to endure fatigue and the want of water. The lama, or 
camel, is much employed fur traversing the Andes ; it is 
dv/arfish but hardy. Oxen and horses are the most com- 
mon beasts of burden in the temperate zone. Oxen are al- 
most wholly employed in the labours of the field, in some 
parts of the United States, while in others, teams of horses 

'are chiefly used. The goat in some parts of Europe, is 
made to labour by treading a wheel, to raise ore or water 



Animal strength not so uniform and precise as other moving powers. The 
efficacy of human strength depends on the manner of its application. Exam- 
ples. Horse power compared with that of other animals. Elephaot. Cam- 
el. Dromedary. Peruvian Lama. Oxen, Horses, &c. 



geneIral remarks upon machinery. 129 

from a mine, and to draw children in little carriages. Dogs, 
in the United States, are sometimes made to perform the 
same service, and also to churn butter, by moving a ma- 
chine. The reindeer is the most serviceable beast of 
draught in the frozen regions of the north, especially in 
Lapland. 

General Remarks upon Machinery. 

346. From what has now been learned, with respect to 
mechanical powers, the pupil v/ill be prepared to understand 
some general principles relating to their use. 

347. These powers do not, in many cases, save labour, 
but they enable one moM by working longer, to do what many 
men might 'perform in a short time. Thus, by means of 
ajackle, having ten folds of rope, one man may raise a 
weight which it would require ten men to raise without pul- 
lies. But if the weight is to be raised a yard, ten men might 
raise it by pulling at a single rope, and walking one yard, 
while the one man at the tackle, must walk until he has 
shortened all the ten folds of rope, one yard each ; that is, 
he must walk ten yards, or ten times as far as the ten men 
did. Therefore to accomplish the same amount of labour, 
we have in the one case the time and strength of one man, 
ten minutes, while in the other, would be required the time 
and strength often men one minute. 

348. A printer with his screw, may press a sheet of 
paper against types, so as to take off a clear impression, 
whereas without the press, the strength of fifty men w^ould 
scarcely be sufficient; and these fifty men would be idle 
and superfluous, except just at the time when the press- 
work is to be done. The screw may therefore be said to 
do the work of fifty men, since it saves the expense of 
keeping this number to perform what one man can now do. 

349. Machinery often enables a man to exert his whole 
strength in cases, when without this assistance, he could 
employ but a part of it. Thus in winding silk or thread, he 



What general principles may now be understood'? Mechanical power ena- 
bles one man to do the labour of many. Examples. Advantaoo of machinery 
in printing. Cases in which machinery enables a man to exert his whole 
strength. 



130 NATURAL PHILOSOPHY. 

might turn oiie spool, with one fiftieth part of the force which 
he was capable of exerting. By means of machinery he 
might turn fifty spools, in the same time that without it he 
could one, though with an increased amount of exertion. 

350. Females are greatly indebted to machinery, which 
has relieved them of much severe labour. Until within a 
few years since, all the wool manufactured in the country, 
was carded by females, in a slovv^ and laborious manner 
With hand cards. The wives and daughters of farmers, 
could find little leisure for intellectual cultivation, or even for 
necessary rest, amid the various duties of a household, and 
the slow operations of domestic manufactures. The inven- 
tion of the carding machine enables them, for a few shillings, 
to get as much wool carded, (and m a far better manner 
than they could do it by hand,) as it would have taken them 
many wearisome days and weeks to accomplish. 

351. There is also an improvement in the common 
spinning wheel. An additional small wheel, and short band 
near the spindle, so much increases the velocity of the mo- 
tion which twists the thread, as grcEitly to .facilitate the 
operation of spinning by hand. But carding, spinning," and 
weaving, are now mostly performed through the agency of 
complicated machinery, moved by water or other power. 
The tending of these machines affords support to vast num-. 
bers of individuals. A wonderfully increased value is hereby 
given to human exertions. A few persons, by the aid of 
machinery, are able to manufacture more cotton or woollen 
cloth, within a given time, than multitudes could do in the 
old methods. The articles for common clothing are now 
afforded at a very cheap rate, so that the poorest people, 
with any degree of industr}^, can supply their necessary 
wants. 

352. Macliinery is useful in changing the direction of mo- 
tion. The two varieties of motion most common in Mechan- 
ics, are the rectilinear and circular. In rectilinear motion, 
the several parts of a moving body proceed in parallel 
straight lines with the same speed. In circular motion, the 
several parts revolve round an axis, each performing a com- 



Females are indeUed to macliinerj-. The cardins^ machine. The double wheel 
head. Carding, spinning, and weaving by machinery. Direction cf morion 
changed. Motion rectilinear and circular. Operation of these motions. 



REMARKS ON MACHINERY. 



131 



plete circle, or similar parts of a circle, in the same time. 
Each of these two kinds of motion may be either continued 
or reciprocating. In a continued motion, the parts 7nove 
constantly in the same direction. In reciprocating motion^ 
the parts 7nove alternately in opposite directions. 

353. Continued rectilinear motion, is seen in the flowing 
of a river, the blowing of wind, the motion of an animal upon 
a straight road, and in the perpendicular fall of bodies. 

354. Reciprocating rectilinear motion is seen in the rod of 
a common pump, as it rises and falls, and in the piston of a 
steam engine. 

355. Continued circular motion, is that which is seen in 
the revolving of wheels of all kinds, and in turning a crank, 
as in the windlass used for drawing water. 

356. Reciprocating circular motion, is seen in the pendu^ 
lum of a clock, and the balance wheel of a watch. 

357. By means of machinery, a power having any one of 
these four varieties of motion, may be made to communicate 
either the same kind of motion, changed in its velocity or 
direction, or either of the other kinds of motion which we 
have enumerated. 



Pi?. 102 




358. The continued rectilinear, or straight 
forward motion of water, produces the cir- 
cular motion of the water wheel. 



Examples of reclilinear molion. Examples of reciprocating rectilinear nio. 
tion. Examples of circular motion. Examples of reciprocating circular motion. 
The various kinds of naotion may be modified and varied. Ezample first. 




Ig2 NATURAL PHILOSOPHY. 

Rectilinear Mofioii changed to Circular, 

Fhjr, 103. 



359. The straight downward pressure 
of the foot upon a board, communicating 
by a crank with the common spinning 
wheel, causes its rotary motion. 



360. The turning lathe of the carpenter, is also an in- 
stance of straight motion changed into circular. 

361. The alternate rising and falling of the piston of a 
steam engine, by means of a crank, communicates motion to 
the wheels. 

Circular motion changed to Rectilinear. 

362. The turning of an axle will wind up a rope, and thus 
lift a weight in a straight line. In the screw, the lever, 
which has a continued circular motion, causes the screw to 
advance with a continued rectilinear motion. 

363. Machines of different kinds are in use in every fam- 
ily, as the churn, washing machine, apple paring machine, 
coffee mill, and clock ; while every town and village, has its 
grist mills, saw mills, and carding machines, and no one can 
go far in any section of our country, without hearing the bu- 
sy hum of the " factory," where woollen and cotton cloth, 
and paper, are produced at a rapid rate. 

364. The observing 5''oung student in mechanical philos= 
ophy, can therefore never be at a loss for examples or illus- 
trations of the science ; whether he travel by land or by wa- 
ter, or sojourn in city or country, he will see in every motion 
around him, either of animate or inanimate objects, some- 
Example second. Example third. Example fourth. Example fifth. Ma- 
chines for family use — And for other purposes. Reflections. 



THE PENDULUM. 133 

thing to remind him of the laws and principles which he has 
already learned, or to suggest new applications of them. 
Even his own frame, in every motion of its muscles, is a 
living and moving example of the great laws of mechanical 
philosophy. 



LECTURE XVIL 

THE PENDULUM. 

364. The oscillation, or vibration of the pendulum, is the 
effect of gravitation. This simple instrument not only of- 
fords the means of ascertaining the variation of the force of 
attraction in different latitudes, and Xhus furnishes a standard 
of weight, but its vibrations give the most accurate method of 
measuring time. 

365. Let P C represent a pendulum 
consisting of a heavy body, P, attached 
to a thread or wire, P C, which is fast- 
ened to the point C, and is movable 
around it. If the body P were left free, 
or not retained by the thread, it would 
'fall in the line P B vertical to the earth's 
centre ; but being thus retained, it is 
forced tcTdescribe the arc P A, 'which is the segment of a 
circle, of which P C is the radius. The body P acquires a 
velocity in falling through P A, that has a tendency when it 
arrives at the point A, to carry it off in the tangent A D ; but 
being prevented from moving in a straight line by centripetal 
force, viz. that of the string, which continually draws it to- 
wards the centre, it is forced to describe the curve A E. In 
the pendulum we see an illustration of the effect of gravita- 
tion in accelerating and retarding motion ; thus from P to A, 
or downwards, the pendulum moves with accelerated motion ; 




Cause of oscillation. Use of the penduluui. Motion of the pendulum desci 
bed and explained. 

12 



X34 NATURAL PHILOSOPHY. 

while from A to E, or upwards, the motion is retarded, until 
the force of projection being overcome by gravitation, it de- 
scends with accelerated velocity towards A. Were it not 
for the resistance of the air, and the friction of the suspend- 
ing line on the point of suspension, or some other accidental 
obstruction, a pendulum once set in motion would, like the 
planets in their orbits, continue its motion forever. 

366. Each swing of the pendulum is called a vibration, or 
oscillation ; these vibrations will be described in equal times, 
whatever be the extent of the arc passed through. Thus 
this simple instrument, by means of its connexion with a few 
wheels, has become a time-keeper, warning us at every vi- 
bration, that the number of ouf allotted moments upon earth 
is becoming less. 

367. The philosopher Galileo was led to the invention of 
the pendulum, by observing the motion ofa chandelier hang- 
ing from the wall of a church in Pisa. Seeing that, when 
put in motion, it vibrated with uniformity as to time, he was 
led to make experiments which established what is termed 
the law of Isochro7iism,* or equality of time. 

368. Though the resistance of the air passed through by 
the pendulum at each vibration, does in fact weaken the vi- 
bration, so that every successive arc of a circle described, 
becomes somewhat lessened ; yet, as the rate at which it 

Fig. 105. ^ moves becomes slower, as the space 
passed through is shorter, a large vi- 
bration is performed in the same time as 
a smaller one. Thus the ball B, sus- 
pended from the point A, moves from 5 
to 5, from 4 to 4, &c. in the same time 
^^ k\^^ ^^^om 1 to 1 ; for, in proportion as 

\5A^ 1 \%^^^^^'^^ ^''<^ described is more extended, the 

^^'■^"-^^t: I — '■""^ stppnpr arp it« hpcrinninn- nnrl pnr]inrr 



Steeper are its beginning and ending, 
^ and the more rapidly the pendulum 

fails, and passes through the intermediate space. 

369. The complicated machinery of a clock we shall not 

' From the Greek isos, equal, and kronos, time. 

Vibrations in equal times. Origin of Isocluonism. Cause of the equal times 
of vil)ratioriS. 



THE PENDULUM. 135 

attempt to describe, Ever}^ person of common observation 
has noticed the wheels, weights, and pendulum, which be- 
long to this curious piece of mechanism. The weight is at- 
tached to a cord which is wound round a cylinder called the 
barrel, this barrel is movable on an axis. The suspended 
weight, pressing dmvn wards by the force of gravitation, draws 
upon the cord, which gradually unwinding, moves the barrel. 
This motion is communicated to a small wheel, which in its 
turn communicates motion to a series of large and small 
wheels. Thus, the office of the weight is to turn all the 
wheels, and keep the pendulum (the axis of which is attached 
to the machinery,) in motion. When the pressure of the 
weight has drawn all the cord from the barrel, the clock 
will stop. It may be ''set going," or put in motion again 
by ^^ winding up,^' that is, raising the weight by winding the 
cord around the barrel wheel, so that its gravitating force 
may again act upon the machinery. 

370. We have already observed that a pendulum once 
set in motion, would continue to vibrate were it not for cer- 
tain opposins!' forces, viz. friction, and the resistance of the 
air, and would thus, without die aid of machinery, afford an 
exact measuie of time, and an instance of perpetual motion. 
But some degree of force must be applied, to counteract the 
impediments to its continued motion ; and this force is obtain- 
ed in the clock, as we have seen, by i\\e pressure of the weight 
upon the cord. 

371. The main spring of a watch, answers the same pur- 
pose for communicating motion to its wheels, as the cord and 
weight of a clock. The watch spring is coiled up in a spi- 
ral manner, within the large barrel wheel ; to this wheel 
one end o[ a chain is fixed, and wound round the barrel 
upon the outside. The other end of the chain is fixed to a 
solid, cone shaped wheel, called the fusee. The force ex- 
cited by the main spring in the barrel, to unbend itself, will 
make the barrel turn in a contrary direction to that by which 
it was bent up. This force of the spring unbending itself; 
like the cord and weight of the clock, being communicated 
to the wheels, sets them in motion. And while the motion 
of the wheels of the clock is regulated by the pendulum, the 

Moving power in a clock. Force vvliich keeps the pendulum in niotion. Mo- 
ving power in u watch. 



136 NATURAL PHILOSOPHY. 

motion of those of the watch is governed by the halanct 
wheel, 

372. The motion of the hands is produced by the opera- 
tion of ingeniously contrived wheels, fitted with teeth or cogs, 
so as to give motion to other wheels. One wheel having 
sixty such teeth, turns round once for sixty beats of the pen- 
dulum of the clock The pendulum being so graduated, as 
to beat seconds, one revolution of this wheel is therefore 
made in sixty seconds, or one minute. An index fixed on 
the axis of this wheel, and projecting through the dial plate, 
is called the second hand of the clock. Another wheel is so 
connected with this, and the number of teeth so proportion- 
ed, that it turns sixty times slower, in order to cany a min- 
ute hand upon its axis, and another wheel by moving twelve 
times slower than that which carried the minute hand, is fit- 
ted to carry upon its axis the hour hand. 

373. Though " a clock is nothing m6re than a piece of 
mechanism for counting the swings of a pendulum," its ad- 
vantage to mankind is incalculable. Before its invention, 
men made artificial divisions of time in various imperfect 
methods, as by observing the regular dropping of water, the 
running of sand in the hour glass, and the shadow upon the 
sun-dial. 

374. The length of the pendulum influences the time of its 
vibration. Long pendulums vibrate more slowly than short 
ones, because in corresponding arcs of circles, the ball of the 
long pendulum has a greater distance to pass over without 

having a steeper line of descent. If a pendu- 
lum, h a, be twice as long as another extend- 
ing from h to e, it has twice the length to fail 
in its descending arc c a, as the other in its 
arc de ; its movement will, therefore, be pro- 
portionably slower, according to the laws of 
gravitation, that is, the time of the vibration 
will increase, as the square root of the length of 
the pendulum increases. If a pendulum one 
yard long, would make one vibration in one second, a pen- 
dulum 1.4 of a yard long, would vibrate half seconds, 
four yards long, would vibrate once in two seconds, nine 



Motion of the hands of a clock, and how produced. Different modes of divi- 
ding time. Effect of lengthening or shortening the pendulum. Rule. 




THE PENDULUM. 137 

yards long in three seconds, &c. ; for one fourth is the 
square root of one half, 2 of 4, 3 of 9, and so on. 

375. The pendulum being usually of metal, is liable to vari- 
ations in length, from changes in temperature. In summer, 
being dilated or lengthened by heat, ii vibrates more slowly 
than in winter, when, owing to the loss of caloric, it has be- 
come shortened. Though the difference in the length of 
pendulums, and their consequent variation in time, is slight, 
It is of some importance, and various methods have been in- 
vented for obviating .this irregularity. The length of a pen- 
dulum for vibrating seconds is, in our latitude, about thirty- 
nine inches. 

376. Since the vibration of the pendulum depends on the 
force of gravity, it follows that pendulums of the same length 
v/ill vibrate quicker when the force is greater. As the 
force of gravitation decreases as the distance from the 
earth's centre increases, it follows that the vibration of the 
pendulum is slower upon the summit of a high mountain than 
at its base. Any change in the force of the earth's at- 
traction would at once vary the motion of the pendulum, and 
prevent clocks from measuring time truly. In mines and 
deep caverns of the earth, though the pendulum is nearer the 
earth's centre, the weight or gravity of the great mass of 
matter above, counteracts the central force, and attraction is 
therefore less than at ihe surface ; the pendulum of course 
vibrates more slowly. 

377. At the equator, the oscillations of the pendulum are 
slower, than at any other point on the surface of the earth. 
This is owing to the form of the earth, which is bulging at 
the equator, and flattened at the poles. Therefore the pen- 
dulum at the equator is farther from the centre of the earth. 
The centrifugal force arising from the earth's motion being 
also greater at the equator, has an effect to counteract the 
force of gravit}'". 

378. As the attraction of gravity is in proportion to the 
mass of matter, the quantity of weight attached to the pen- 
dulum, or the weight of its ball, has no effect upon the speed 
of its vibration, except that which results from the resistance 

Effect of temperature upon the ppiidiiluin. Lonotli of a ])en(luluiii for se- 
conds. Why the penduhim vibrates slowly on liigh inouatains and in mines, 
vibration at the equator= Why slower? We'ght of the ball does not etfect 
vibration. 

12* 



138 NATURAL PHILOSOPHY. 

of the air. Experiments upon the pendulum, to be perfectly 
accurate, should be made in a vacuum; or in a space from 
which the air is excluded. 

379. The pendulum is net only of importance in regulating 
our divisions of time, and thus enabling us to systematise the 
business of life, but it affords the only sure mode of determin- 
ing the variation in the force of gravity, in different latitudes, 
and at different heights. While it serves to amuse the. child 
by its regular and continuous motion, it furnishes problems 
to the philosopher, the solution of which requires the most 
intricate and profound mathematical calculations. 



LECTURE XYIIL 



LOCOMOTION. 

380. Before closing our investigations of mechanics, we 
will make a few remarks upon the wonderful improve, 
ment, which this science, aided by chem.ical discoveries oF 
the nature and powers of steam, has effected in the rapidity of 
locomotion.* 

38i. Let us imagine the state of our own country, when 
our ancestors planted themselves here. The Indian had no 
roads, and he needed none. His wandering life led him to 
traverse mountains and forests for game, and to follow the 
winding stream for fish= Fine roads and convenient carria- 
ges, would have been to him superfluous. In the long jour- 
ney from Plym.outh to Windsor, undertaken by our pilgrim 
fathers, they travelled through a trackless wilderness, bear- 
ing the good wife of their minister, Mr. Hooker, on a litter. 
Such was the first rude carriage w^hich passed from Massa- 

■* From, two Latin words, locus, place, and motio, motion, sigTiifying motion 
from a place. 

Why should experiments be made in a vacuum? Mechanics connected with 
locomotion. Former stale of our country in regard to roads. Journey from 
Plymouth to Windsor. 



LOCOMOTION. 139 

chusetts to Conneclicut. Several weeks were required to 
perform the journey. There were no bridges across the • 
streams, and the weary travellers must seek for fording pla- 
ces as accident might lead them ; searching their way 
through the defiles of mountains, meeting continually with 
obstacles, which obliged them to retrace their steps, and 
take a new direction. In , perils from savage men and 
ferocious beasts, and deprived of nearly every comfort, they 
encamped, when night overtook them, beneath the canopy 
of heaven, trusting in the protection of that Being, whom 
they sought to worship in sincerity and truth. 

The first roads and bridges, constructed in our countryj 
were of a rude and temporary nature. Carriage roads were 
unknown long after paths were traced, leading from one 
settlement to another. 

. 382. Science furnishes rules and principles for the con- 
struction of roads ; and in these days, when new roads are 
to be made, they are not left to chance or the rude skill of 
the ignorant ; but civil engineers are called upon to surve}^ 
and graduate them, according to the laws of mechanical 
philosophy. 

" The province of the engineer, is to surmount the difficult, 
lies presented hy friction, gravitation, collision <ind road sur- 
face. He must consider well the traffic upon the intended 
line of road, and determine whether a saving of tractive 
•power, will compensate for the outlay of capital required to 
form the road. The quality of the road must depend on 
the means of making and supporting it ; and there are situa- 
tions in which it would not be judicious, even to attempt to 
make any road at all."* 

383. From common roads for carnages, we have gradu- 
ally passed to canals, McAdamised roads, and rail-ioays. In* 
•canal conveyance, a difficulty has been suggested, founded 
pn the well known law of mechanics, that the resistance of- 
fered hy water to a boat in motion, increases as the squares 
of the velocity. But an English writer suggests, that if ca- 
nal boats were differently constructed, their speed might be 

' Gordon on Locomotion. 



Science important in the constructioxi of roads. Circumstances to be consid- 
ered by the engineer. 



140 NATURAL PHILOSOPHY. 

greatly increased, without increasing tlie resiciance of the 
.water. He would have the horizontal, or propelling force, 
30 great, as to allow httle opportunity for the force of gravi- 
tation to act upon it, and thus cause the boat to skim the 
surface of the water, rather than, by suffering it to become 
deeply immersed, to have the resistance of a large body of 
the fluid to overcome. Thus, suppose a number of cannon 
balls laid in. a single tier, upon a level surface, in contact 
with each other ; should one attempt to move the further- 
most ball, by a slow motion in a line with the others, he must 
communicate motion to them all, and therefore be obliged 
to use a force much greater than would have been necessa- 
ry if with a quick motion, he had drawn the ball above 
the others, and moved it over their surfaces. 
; It is said, that on the Paisley canal in Scotland, boats are 
moved by horse power, at the rate of ten miles an hour ; 
and it is suggested that by the use of steam instead of ani- 
mal power, the velocity may be increased and the expense 
of locomotion lessened.* 

384. McAdamised roads are intended to prevent the re-, 
sistance of surface. Stones broken into small fragments 
are laid upon the road to the depth often inches. Mr. Mc 
Adaui considered, that a road thus constructed, would 
be smooth and durable ; and that the nature of the soil be- 
low the coating of broken stones, was of no importance. 
This kind of road, no doubt, is an improvement upon the 
ordinary turnpike roads. But it does not answer all the 
valuable purposes supposed by its projector. It is found to 
be, not only exceedingly expensive in the outset, but to re- 
quire alsoj almost constant repairs. 

* The work of Gordon, on locomotion, publislied in London, contains many 
valuable suggestions, which might in this day of miprovement, prove useful in 
our own country. Could Ave see on our great western canals, packets moved 
swiftly by steam, the scene would be far more pleasant than that exhibited by 
the slow motion of jaded animals ; and a great advantage would be afforded in 
the iacreiis3d facilities for locomotion and ti-ansportation. But it remains to be 
proved that Mr. Gordon's plan of avoiding the resistarice of a large portion of 
fluid can be acted upon by means of any construction of boats, or peculiar mode 
of applying the motive power. Dr. Lardner, and some other scientific men, do 
not admit the .practicability of any plan of the Irind. 



Supposed dilSculty in canal conveyance. Hov; obviated. McAdamised 
roads. 



LOCOMOTION. 141 

385. In the construction of railroads, and the application 
of steam power to locomotion by land, we see the greatest 
triumph of modern improvement. Instead of the nerves and 
sinews of animals, strained to their utmost extent to drag 
their ponderous loads, is substituted the power of the light 
elastic steam ; air agent which can suffer no pain, and which 
consumes no food. About seventy years ago, Oliver Evans, 
an unlearned American mechanic, happening to make some 
observations upon the elastic power of steam, conceived the 
idea that it might be turned to some account in moving ma- 
chinery. He was confirmed in his opinions, by experiments. 
But when he predicted, that " the child was then born, who 
would pass in carriages propelled by steam, at the rate of 
at least fifteen miles an hour," he was thought to be insane. 

386. Rail roads, were first made in England ; they are 
-now numerous in our own country, connecting many of the 
most distant icities of the union ; by means of these, and the 
aid of steam boats, a rapid communication and intercourse 
is maintained throughout the country. The traveller leaves 
New York in the evening, lies down in his berth in the steam 
boat, and in the morning finds himself at Albany, having 
travelled one hundred and sixty miles during the night. He 
may then step into a rail road car, and be carried to Sara- 
toga springs, forty miles farther, to breakfast. The Dutch 
settlers of New Amsterdam (as Nev/ York was first called,) 
considered the dangerous voyage up the Hudson to Albany, 
well performed if made in one or two weeks ; and no more 
than five years ago, it was thought a good day's ride from 
Albany to the Springs. 

387. Now, instead of measuring distance by miles, we 
compute by hours. New York is brought within fourteen 
hours of the Springs, instead of being as many days distant. 
The effect of this connexion of places, once considered distant, 
is very important, upon the wealth, comfort, and improvement 
of society. The merchant, after purchasing his goods in 
one of the large cities, is not obliged to lie out of his capital, 
while they are, day after day, moving slowly onward as in 
the old mode of conveyance. If there is a deficiency of any 
article in one part of the country, there will be a rapid pres- 



Rail Roads Rapid travelling. Ellect of rapid cominunication upon the pros- 
perity of the country. 



142 



NATURAL PHILOSOI^HY. 



sure of it flowing from those places where it is more abun- 
dant.- A quick and general circulation of the produce of 
the earth ; of articles 'of commerce, and of literature, is to a 
nation, what the healthy circulation of the blood is to the 
human system. 

We shall hereafter consider the manner in which steam 
is made to act as a moving power. We are now merely to 
notice its application to land carriage. 

388. Rail roads, or rail-ways, are made by laying hori- 
zontal bars of iron for the wheels to run on. The wheels 
are confined within the track by a groove in the rails. 
The figure shows a locomotive engine, with the wheels 

Ficr. 107'. upon the iron rail- 

way. The engine 
is followed by a ten- 
tier, containing the 
engineer, with a 
ii lJilill jimUBiL supply of fuel and 

Tj- , , _^- y ^^^W^ w^tPv. The train 

^ Ela tin di] ^ 25 BE of carriages attach- 
ed, varies in number according to the number of passengers 
and amount of goods to be conveyed. The carriages for 
passengers are usually called cars. 

389. When horses are the motive power, it is not desira- 
ble that the wheels of the carriage to which the horse is har- 
nessed, or those of the train following, should take hold of 
the rails ; on the contrary, the less they adhere, the more 
easy it will be to move the train. But when a locomotive 
is to be impelled by the action of the steam engine, in 
turning the wheels, if the resistance by gravity and friction 
be greater than the force with which the wheels adhere to the 
rails, the engine will only revolve the wheels to which it is 
geared ; these will turn upon the rails, while the locomotive 
and whole train attached to it, will remain stationary. To 
prevent this, different contrivances have been resorted to. 

It has, hov/ever, been found in practice, that, for the ordi- 
nary inclination of rail roads, (to the extent of about thirty 
feet per mile^) the v^/heels may be so constructed as to move 




Mode of constructing rail-ways. Adhesion of the wheels of the carriage to the 
rails d disadvantage, when horses are the moving power. The case is difierent 
when a carriage is moved by a steani engine. 



Locomotion. 143 

a train of cars by their mere adhesion to the rails. One of 
the first expedients for increasing the adiiesion of the wheels 
to the rails, without incurring any additional loss by more 
weight or friction, was to gear the four wheels of the loco- 
motive car together, so as to have the friction of all of them 
upon the rails ; for, if the piston of the engine is connected 
by gearing, with' only one pair of wheels, a resistance in 
the other wheels of the engine, and by the whole train, only 
equal to the friction of those two wheels, can be overcome. 
By gearing the piston of the engine with the four wheels 
of the locomotive, by means of an endless chain passing 
round the two axles upon two cogwheels, or by otherwise 
gearing the four wheels together, or to the piston, the hold* 
of the wheels on the rails is doubled. 

390. The locomotives vary in weight from three or four 
to ten or eleven tons. A locomotive, with its apparatus^ 
and appendages, weighing four and a half tons, will adhere 
to the rails with sufficient force to draw thirty tons weight on 
a level road, at the rate of fifteen miles per hour, and seven 
tons up an ascent of fifty-five feet in a mile ; at a slower 
rate, it will draw a greater weight. The slower the rate of 
travelling is, the greater the weight that may Le supported 
by the same wheel, v/ithout injury to the road from shocks. 
Gare should always be taken, however, to proportion the 
weight to the size and strength of the rails. 

391. Another step in locomotion, which seems about to be 
taken, is the construction of steam carriages to run on com- 
mon roads, which shall go up hill and down without any aid 
from machinery, other than the proper regulation and ad- 
justment of the motive power. In England many trials 
have been made to this effect ; and a committee appointed 
by the House of Commons, have reported favourably upon 
the project. The Committee give it as their opinion, that 
the advantages of steam power are not confined to the 
greater velocity obtained, or the expense, as compared with 
that of horse power. But they think, in relation to the use 
of horses, that danger as well as expense, is increased by 

* The hold of the wheels on tlie rails, is by engineers called the bite ; it con- 
sists in the/orce of adhesion, between the wheels, and the iron rails. 

Mode of increasing the adhesive force. Power with which locomotives ad- 
here, and the efiects cf this adhesion. Steam carriaares for common roads. 



144 NATURAL PHILOSOPHY. 

greater speed. In steam power, on the contrary, there is 
no danger of being run away with, and the risk of being 
overturned, is greatly diminished. Steam, is found to be 
perfectly controllable, and capable of exerting its power to 
retard the motion in going down hills. It can be perfectly 
under the controul of the person who guides the carriage, and 
can be stopped or turned with the slightest exertion, and un- 
tler circumstances where horses would be unmanageable. 
Sounds or sights, can have no ppwer to affright this un- 
conscious agent, which labours so effectually for mankind. 

392. Such being the views of men of science, we may 
live to see the day, when the farmer's plough, and market 
waggon, the pedler's cart, stage coaches, and private carria- 
ges will h& moved by steam power, and when steam for the 
purposes of locomotion will be as common in every family 
as now is a coffee-mill, a patent churn, or a v/ashing ma 
chine. 

Steam power considered more safe than horse power. May be perfectl}^ under 
controul. Fros]iectiveyiew of the use of steam for locomotion. 



PART III. 

HYDROSTATICSo- 



LECTURE XIX. 



MECHANICAL PROPERTIES OF LIQUIDS. 

393. There are, in nature, three distinct forms under 
which substances exist; solids, liquids, and gases ; wood, 
water and air, are examples of each class. Many of the 
mechanical laws which apply to solid bodies, and which we 
have already considered, govern liquids and gases in an 
equal degree ; but as the two latter have properties peculiar 
to themselves, it follows that each class is subject to its own 
laws. 

394. Under the general name o^ fluids are included Z^- 
qidds and gases ; the former an; called non-elastic fluids, 
the latter, elastic fluids. 

395. The name of non-elastic fluids was given to liquids 
from the supposed fact, that they were in no degree elastic, 
or compressible. Common air, steam, and other elastic flu- 
ids, are easily compressed, and on removing the pressure 
they expand to their original dimensions. This may be 
proved by squeezing an inflated bladder ; a leather bag, or 
Strong bladder, filled with water, and secured so that none of 
the liquid can escape, may be burst by forcible compression, 
but cannot be made to exhibit any sensible degree of contrac- 
tion. Water from its powerful resistance to pressure on all 
sides, was long considered as perfectly incompressible. An 
experiment made by some philosophers at Florence, in the 

Substances exist wndoy t'oree forms. Liquids and gases subject to peeuliar 
laws. Fluids, how divided ] Liciiiids fohnevly supposed to be incompressible. 

13 



146 NATURAL PHILOSOPHY. 

sixteenth centuiy, confirmed this opinion. The experimen& 
was this : a hollow globe of gold was filled with water, and 
being closed up, was subjected to the powerful action of a 
screw press. The water forcing its way through the pores 
of the dense metal, appeared like dew on the oater surface 
of the globe. I'hough this experiment was at the time, and 
long after that period, considered as conclusive proof, that 
water cannot be compressed, later trials have shewn, that 
though its resistance to pressure is very great, it will, under 
a certain weight, yield in some degree. Experiments by 
Mr. Perkins, before the Royal Society of London, proved 
that a weight of 2003 atmospheres, (or a weight 2000 times 
greater than that of the atmosphere,) diminished the bulk of 
water l-12th part. 

But so inconsiderable is the degree to which liquids can, 
by any ordinary force, be compressed, that in all calculations 
respecting their action, they are regarded as incompressible 
fluids. 

396. Solid bodies are subject to the power of cohesive at- 
traction in a much greater degree than liquids; and the lat- 
ter, in a greater degree than gases. The parts of a solid 
are connected together, so as to form one whole ; their force 
of gravity is therefore centred in one point, which ifsupport= 
ed, prevents the whole from falling. In fluids (although 
each atom has its own centre ofgravit}^) the parts have not a 
common centre of gravity, therefore as soon as a vessel is fil- 
led with any liquid, each additional drop runs off" at the sides. 

397. The sa?ne suustance may exist hi the form of a solid ^ 
a liquid, at a gas, or vapour. Ice is solid ; expose the same 
to the influence of heat, and it assumes the liquid state ; an 
additional quantity of heat causes this liquid to become 
steam or vapour. Mercury is commonly seen in the form 
of a ver}^ dense liquid ; but it may like water be condensed or 
frozen by exposure to a very low temperat'ire, and made to 
boil or evaporate, by subjecting it to a great degree of heat. 

We shall now consider the mechanical laws of liquids, or 
Don-elastic fluids. 

39S. The term Hydrostatics, is from two Greek words, 
udxyr, water, and states, standing ; the science is that depart- 

Experiments of Philosojihers at Florence. Experitnents of Perkins. Li- 
quids have less cohfsion tiian solids. Proof. The same substance may eiist 
uitFerent forms. What is Hydrostatics 1 



HYDROSTATICS. 147 

nient of Natural Philosophy, which treats o[ the weighty 
pressure, and eqiuuhrium of liquids. 

399. Liquids afford an example of a state, in which the at- 
traction of molecules (or cohesive attraction) is exactly bal- 
anced by the repulsive principle, heat. Thus, water, by losing 
a certain portion of caloric, or the matter of heat, is given up 
to the power of molecular attraction ; and its particles cohei> 
ing, it becomes a solid. But when caloric overcomes its 
antagonist principle, the particles ofvvater are driven to a 
greater distance, and the liquid changes to a light and ex- 
pansive vapour Oil deprived of caloric, congeals into a 
solid ; by the addition of caloric, it becomes the gas, knov/n 
iu chemistry, as olefiant or oil-gas. 

400. The particles in- liquids are freely movable an^.ong 
each other ; and yield to t]:ie least disturbing force. These 
particles are supposed to be round and smooth, because they 
move easily, and v/ithout fiction. This supposition ac- 
counts tor sonie properties of liquids, which could not other- 
wise be vv'eil explained. For instance, water v/ill take up a 
certain quantity of sugar without being increased in bulk ; 
again, a certain portion of salt may be added, and yet the 
original bulk of the water will remain the same. In order to 
Pig- in-^ illustrate this, let us suppose a vessel (fig. 104,) to 

be filled with cannon balls, it is evident that it can 
hold no more of these balls, but a quantity of small 
shot might find their way into the spaces which 
vv^ould exist between the large balls, and when no 
no more shot could be added, sand, or ashes might 
be introduced to fill up the spaces between the shot, 
and water might afterwards be added to fill up the sj)aces 
between the particles of sand. It is a Vv"eil known fact, that 
a cask filled with ashes, will receive a large quantity of 
water. Now admitting the spherical form of the parti- 
cles which compose liquids, we can perceive the reason that 
some will receive into the spaces between them, smaller par- 
ticles of other substances. 




Attraction and ivpnl.=;ion balcmced in liquids. Part'k'los of liquids. Liquids 
ivill take up purtioua ofcerlauii substances witliout ixuy iacroase of bulk. 




148 NATURAL PHILOSOPHY, 



Pressure of Liquids. 

401. Liquids press not only dowmcards, like solids, but 
upwards, and sideways or laterally, and i\\\s, pressure is equal 
in all directions. 

402. We will first shew the upward pressure of liquids. 
Fia-. lOo. Let ABC. represent a bent tube of glass. Now if 

by means of a funnel, you pour sand into one side of 
the tube A, you will find, that the sand after filling 
the lowest part of the tube, will rise until the side A 
B is full, after which, if sand continues to be poured- 
into the funnel, it will run over the top of the tube at 

A. Now instead of sand, if you pour water, or any 
other liquid, into the tube, at the mouth A, 5 ou will find the 
fluid to preserve a level on both sides of the tube; a small 
quantity would fill the bottom and rest at the dotted line, d ; 
an additional quantity would carry the height of the fluid to 
the line e, and another portion would raise it tof. This 
experiment proves the upward pressure of liquids, since the 
water is raised in the side C B, contrary to tlie laws of gra- 
vitation, by this force. 
Figr. 106. 

403. Another simple experiment will serve to 
illustrate the same principle. Let the glass jar, A 

B, be nearly filled with water, while the glass tube, 
a h, is pressed so closely upon the bottom of the jar 
as to prevent the entrance of any of the liquid ; now^ 
if you raise the tube a little, the upward pressure of 
the fiuid in the jar will cause it to rush up into the 
tube until it is on a level with that in the jar. 



4U4. You will perceive in the preceding experiment, that 
the tube a b, is open at the top ; now take it out of the jar, 
and the water is replaced by air, which rushes in to supply 
the vacuum, which would otherwise be left when the water 
escaped. Stop the tube at a, with a cork, and plur'ge it 



Pressure. Upward pressure illustrated. Exp. 1. Exp. 2. What causes 
the water to rise in the tube ? Exp. 3 




HYDROSTATICS. 149 

r.guin into the water; you will see that the liquid has risen 
nu liiuher than b. This is because the tube was filled with 
air and you have learned that matter is impenetrable, or 
that no two substances can at the same time occupy the 
same space. Were it not for the cork at the top of the tube, 
the water, being the heavier substance, would press the air 
upward, and take its place. You will ask, '^ if the tube be 
filled with air, and if this cannot escape, how can the water 
enter the tube f We answer that air is compressible, and 
therefDre the upward pressure of the water has forced the 
air which before filled the tube, into a smaller space ; for it 
is evident that as none has escaped, it must be contained in 
the space between the cork, and the top of the water, b. 
The same quantity of matter being compressed within less 
space, it follows, that the air in the tube is more dense than 
before compression. 

405. Great force is required for the compression of wa- 
ter : let the tube a b, be corked at the top, and filled with a 
coloured liquid ; hold a piece of pasteboard close to. the other 
extremity of the tube, to prevent the escape of the liquid, 
and plunge the tube into the jar of water ; now if you re- 
move the pasteboard, and plunge the tube to any depth of 
water, the coloured liquid will still keep its place, and will 
not, like the air, shew that the upward pressure of the water 
has any power to compress it into a smaller space. 



LECTURE XX 



PRESSURE OF LIQUIDS. 



40G. The lateral, or side pressure of liquids, is equal to 
tjjo pressure either upwards or downwards. That tiie late- 
ral pressure is equal to the pressure downwards, may be 



Why does not the water rise as high as in cxperiniont 2 I Water not easily 
compressed. 

13* 




150 NATURAL PHILOSOPHY. 

p,a._ 1C7 illustrated by the following experiment. Let the 
^ vessel, A B, be filled with water, and two orifices of 
equal dimensions, a and h, made, the one at the bot- 
tom, the other at the side of the vessel. Let the 
water run into two receivers, and it will be found at 
the end of a given time, that the quantity of liquid 
which has escaped, is equal in both receivers. 
'^This proves that the lateral pressure is equal to the 
pressure downv/ards : otherv/ise the liquid would flow out 
faster from the orifice at the bottom of the vessel, than fi'om 
that at the side. You will observe that the opening at the 
side (see the preceding figure) is made quite at the lower 
part of the vessel, for were it higher, the liquid would not 
fiow out with equal velocity ; as the greater the weight of 
the column above, the greater the force of the downward 
pressure ; therefore the 'perpendicular height of the two orifi- 
ces must be equal in this experiment. 

407. From the force of pressure in different directions^ 
water, poured into a bent tube, called a syphon, will stand 
equally high in both sides. 

Fig. los. 408. If the communicating tubes are of different 
diameters, still the fluid stands at the same height 
in both ; therefore a joorti.on of liquid, Jiowever s?naU, 
will resist the pressure of a portion however large, 
and will balance it. 

409. In a common tea pot, we see an illustration of this 
law, as water poured into the body of the 
vessel, will rise to the same height in the 
spout as in the body of the vessel ; and if 
poured into the spout, the small column in 
the latter would still be forced to balance 
the whole column, iii the main portion of 
the vessel. 

Hydrostatic Paradox. 

410. So strange did the law of nature, which we are now 
considering, (section 408) appear, when first discovered, that 



How is tLe lateral pressure of liquids proved 1 Height of liquid in a bent 
tube. In a tube var3nng in diameter. Water at the same height in the spout 
of a tea pot as in the body. 



\U 




HYDROSTATICS. 



15 i 



110. 



philosophers termed it the " hi/droslailc paradox.''^ The word 
paradox, signifies something contrary to appearances, or to 
what we should expect ; — and that a pound of water may 
be nude to sup|)ort a hundred pounds, or any other quantity 
however large, is_an assertion, which at first might well ap- 
pear contrary to reason. This phenomenon may be explain- 
ed on mechanical principles. Opj)osite forces have been 
shezcn io he equal, when their momenta were equal; that is, 
what is wanliig ui weight, may he made up in velocity. In 
mechanics, it is an established law, that the power and weight 
balance each other/ wlien the power moves as much faster 
than the weight, as the quantity of matter is less. Let this 
law be applied to the case which we are now considering. . 
411. Suppose the vessel A, to be ten times 
the size of tiie tube B, then a quantity of wa- 
ter, one inch in height in the tube, would rise 
in the vess-el A, but one tenth part of an inch ; 
or a certain quantity of liquid, v/ould rise 
through a space often inches, in the tube B,. 
while it would rise but one inch in the vessel A. Thus we 
find that there is in reality, nothing more wonderful in the 
hydrostatic paradox, than that one pound at the long end 
of a lever, should balance ten pounds at the shoit end. 

412. 7'he velocity of columns of water when in motion, 
being as much greater in the smaller, than in the larger col- 
umns, as the quantity of matter is less, it follows, that in ves- 
sels of various sizes and shapes, connected with a common 

reservoir, the liquid will 
|,'| rise to the same level, 




FM'. ill. 




in all ; — here the 
loater being considered 
iiiiiiilniiiiiiiiiinniiiiii iiWiiii|i|i f' M, M Mi_ . __ jMiJ the weight, ayid pressure 
the power, the weight and jjovver may be said to be in equi- 
librium, where the fluid is on a level in each of the vessels. 
Thus we find that in all situations, fluids at rest, fmaintuin 
a level, or horizontal position. 

413. The whole mass of a liquid, and the sides of the 
containing vessel, are afected by the slightest compression. 



Explained on mechanical principles. Action of liquids coiupaicd to tliatof the 
lever. Weight and power in equilibrium. 



152 



NATURAL PHILOSOPHY. 




In a quantity of liquid subjected to com- 
pression, the loliole mass is equally affected ; 
if a cork be forcibly driven into a bottle full 
, of water, the pressure will be felt alike in eve- 
ry portion of the liquid, which will equally 
press against the sides of the bottle in all di- 
rections, and it will break at that point which 
is weakest, however situated in relation to the 
mouth, where the force was applied. 
414. The pressure of a column of liquid is according to 
its perpendicular height. 

By this proposition we mean, that the pressure of any 
liquid upon the bottom of a vessel, is not according to the 
quantity contained, hut according to the weight of a perpen- 
dicular column, having for its base the bottom of the vessel, 
and for its height, the deptli of the liquid. If the vessel be- 
come wider towards the top, 
as in A, the pressure is less 
than the weight of the whole 




liquid, it being denoted by the 
shaded perpendicular column, 
the base of which \s a b. If 
the vessel narrow from the base, as at Bjthe pressure is greater 
than the weight of the liquid, it being denoted by the dotted 
lines. When the vessel is throughout of an equal diameter, 
as in C, the pressure on the bottom is equal to the weight of 
the whole liquid. 

415. Suppose the two vessels represented in the figure, 
to have their bases equal, but the 
vessel A, holds twenty times 
more than the vessel B ; that is, 
Vv'hen A is filled, it holds but one 
pint, while B holds twenty pints. 
s Each vessel has a'brass bottom 
D which opens like the lid of a box. 

A pulley, F, has suspended from 

it a weight, E. Let a person hold A, by its sides, and pour 




Does compression on any portion of a fluid, affect other portions in the same 
vessel? Experiment. ^^hdii'\%inear\\.hY ^^ pressure according to heightV^ Sup- 
pose the containine vessel wider towards the top. Suppose the vessel narrower 
towards the top. If the vessel is of an equal diameter throughout. Experiment. 



CENTRE OP GRAVITY. 



153 



in water, until the pressure of the liquid begins to raise the 
weight, and of course to open the lid like bottom, when the 
water will begin to escape. Let the height then be marked, 
at which the surface of the water stood when the bottom 
began to give way. Try the other vessel, B, in the same 
manner, and it wiU be seen that when the water is at the 
height a, that is, at just the same height as in the other ves. 
sel,.the weight will begin to rise, and the bottom to fall. 
Here we see that equal weights are overcome in the one 
case, by twenty pints of water, and in the other case, by 
one pint. 

416. This law, of the pressure of a column of liquid be- 
ing in proportion to its perpendicular height and base, ex- 
plains v/hy a cask when filled with vv^ater 
may be burst by the additional weight of a 
few ounces of water. Suppose A B to be 
such a cask, and C D, a small tube of seve- 
ral feet in length, inserted at the top ; on fil- 
ling the tube with water, the compressive force 
is in proportion to a column, in which the 
height is the height of the tube, and the base 
is the top of the cask, therefore the pressure 

- j^ ,„ .^ U[)on the cask, is the same as if a column equal 

Ifo in diameter to the whole diameter of the cask 

~ fp ^^^^'® carried to the top of the tube: it is not 
surprising, therefore, that such a pressure 
should burst the strongest cask. 

417. Many of the convulsions of nature, evidenced 
in the broken and scattered rocks, may have been 
the effects of hydrostatic pressure. Since- a column of 
water, only a few feet in height, is capable of bursting a 
hogshead by the fjrce of its pressure, what force might not 
be exerted by the water filling a fissure in a mountain, which 
should extend downward some hundred feet ! " Thus sup- 
pose in the bowels of some mountain there should be an 
empty space often yards square, and only an inch deep, on 




What, does the experiment prove? Expcriinont. Why is a small qnantity 
of water in the tube, capalile of ucUwg wiili sj powerful a pressure'' Etll-ct of 
water pressure in rending mountains. 



154 



NATURAL PHILOSOPHY. 
Fior. 116. 




an average, in which a thin layer of water had lodged, so as 
to fill it entirely ; and suppose, tliat in the course of time, a 
small crack of no more than an inch in diameter should be 
worn from above, 200 l^eet down to the layer of water ; if' 
the rain were to fill this crack, the mountain would be sha- 
ken, perhaps rent in pieces, with the greatest violence, being 
blown up with a force equal to the pressure of above 5022 
tons of water, though only 2 1-2 tons altogether had been 
actually applied."* 

Hydrostatic Bellows. 

418. The hydrostatic, or water bellows, is an article of phi- 
losophical apparatus, v/hich* illustrates in an interesting man- 
ner several of the princijjles with respect to the pressure of 
fluids, which we liave endeavoured to explain. A long tube 
communicates with the body of the bellows ; this consists of 

* See Treatise on Hydrostatics, Librai'}' of Useful Knowledge. 



Explain the principle on which the hydrostatic bellows is constructed. 



HYDROSTATICS. 



151 




Fig. 117. two oval boards, connected by folds of leather, 
fi.^^^like the connmon bellows. When the tube is 
filled with water, the pressure upon the upper 
part of the bellows will be such as not only to 
raise the board, but to sustain heavy weights 
placeii upon it. The force of the pressure, 
(when the tube is full,) will be equal to the 
Weight of a column of water, whose base is as 
the surface of the bellows, and whose height as 
the length of the tube. 

419. it will readily be perceived that the 
pressure of a certain quantityof water, may be 
increased by making the circumference of the bellows lar- 
ger, and the tube smaller and longer; as by so doing, the 
base and height of the column \yill be enlarged. If the tube 
hold an ounce of water, and have an area equal only to one 
thousandth of that of the upper board of the bellows, one 
ounce of water in the tube, will raise or balance a weight of 
a thousand ounces, resting on the bellows. 

420. If mercury were substituted in a similar machine, 
for water, the eilect of the fluid pressure would be fourteen 
times greater, because the same bulk of mercury is fourteen 
times heavier. Air, which is an elastic fluid, may also pro- 
duce powerful effects in the same manner ; if a bellows were- 
sufficiently large in diameter, a man standing upon it might, 
:by blowing into the tube with his mouth, raise his own weight 
by the upward pressure of the air acting upon the bellows. 

421. The i^riiyciple of hydrostatic pressure has been ap- 
plied to the construclion of a very powerful press, called the 
hydrostatic, or ii'afer-j>re.ss. So great is the force thus ob- 
tained, that with a machine no larger than a common tea pot, 
a bar of iron may be cut as easily as a strip of pasteboard 
with a pair of shears. Instead of the tube of the bellows, 
the water-press has a small pump, and for the body of the 
bellows, is substituted a pump barrel and p'ston. 



Force of the pressure of I he column of liquid in the tube. Suppose t'e cir- 
cumference of the beilovvs Aveie l,nL'\'r, aiicl the tube of less diaiuttcr, but e!' 
greater Icnj^tii. ^Vhat Woulil bo iIi ■ ciVcct ol' substituting mercm y for \\Mter in a 
similar niachuie ? Miglit not air bo used instead of water or uicrcury / A;.- 
jilicatioa ol' tbeprinciple of hydrostatic presoure. Power of tlie wai 'r-iness. 



156 



NATURAL PHILOSOPHY. 




422. In the seventeenth century, Pascal, a man celebra- 
ted for learning and piety, discovered the principle of hydro- 
static pressure, and asserted that an 
engine might be constructed, acting 
through the force of a column of wa- 
ter, by means of which, one man, 
pressing on a small piston, might re- 
sist the efforts of a hundred men, 
brought to bear on the surface of a 
large piston. This imaginary ma- 
chine, was termed by its projector, 
"a new machine for multiplying 
forces to any requiied extent." It 

was not, however, until more than a 

century afterwards, that any practical appHcation was made 
of this force. " Bramah's hydrostatic press,^' consists of 
solid masonry, or strong wood work E F, firmly fixed, and 
connected by uprights with a cross-beam. B represents a 
strong table, moving vertically in grooves between the up- 
rights, and supported beneath by the piston A, which works 
Vv'ithin the hollow cylinder L, and passes through a collar N, 
fitting so closely as to be water-tight. From the cylinder 
passes a small tube with the valve opening inwards at I, and 
Disa lever which works the piston of a small forcing pump 
C H, by which water is drawn from the reservoir G, and 
driven into the cylinder L, so as to force it up its piston A. 
At K is a valve, which being reli-eved from pressure, by 
turning the screw which confines it, a passage is opened for 
the water to flow from the cylinder, through the tube M, into 
the reservoir G, allowing the piston to descend. 

42'^. The effective force of such a machine must be im- 
mensely great, combining as it does, the advantages of solid 
and liquid pressure. The amount of the latter is to be esti- 
mated by the relative diameters of the two pistons; so that 
if the piston H be half an inch in diameter, and the solid cyl- 
inder or piston A one foot, the pressure of the water on the 
base of the piston A, will be to the pressure of the piston II 
on the water below it, as the square of 1 foot or 12 inches, 



Drscribe t'le water-press of Brair.ah. jNIode of estimating the advantage of a 
Liter-press of known dimensions. 



HYDROSTATICS. 157 

12X12=144, to the square of i an inch, 5x5=25 ; that is 
as 144 square inches to } of a square inch, or in the ratio of 
576 to 1.* To this must be added the advantage afforded 
by the lever handle of the forcing-pump, depending on the 
relative lengths of its arms ; and supposing the power to be 
thus increased tenfold, the effect of the machine will be aug- 
mented in proportion, or will become as 5760 to l.f 

424. The hydrostatic press is applied to various important 
purposes ; to compress hay, cotton, and other bulky com- 
modities, which may be thus made to occupy on ship-board a 
space twenty or thirty times less than in their natural state. 
It is also used to raise great weights, to uproot trees, and to 
cut hard substances. 

Pressure proportioned to Depth, 

425. The pressure upon any particle of a li- 
quid, is in proportion to its depth helow the sur- 
^face. Thus the inclined column D C, being of 
the same perpendicular height as the straight col- 
umn A C, both exert the same pressure upon the 
base C Suppose e and/" to be half the distance 
from the surfaces A and B, then the pressure up- 
on them is but half as great as upon a particle 
atC. 

426. The cause of this increase of pressure is evident. — 
The fluid atoms being subject to the laws of gravity, the up- 
per layer presses upon the next, which, with double its ov/n 
weight, presses upon the third layer, and thus the pressure is 
constantly increasing with increasing depth. For this rea- 
son pipes for aqueducts should be made stronger in propor- 
tion to their depth, as also the sides of canals, embankments, 

* The pupil will need some knowledge of decimals, to understand this state- 
ment; 5 is the decimal of half an inch, the square of 5 is 25 or ;^ of a square 
inch. Multiplying 144 by 4, we obtain the number 576, and thus the advantage 
here obtained by liquid pressure is as 576 quarters of inches, to 1 quarter of an 
inch. 

t Moffat's Book of Science, London; Chapman & Hall. 

Uses of the water-press. Pressure proportioned to depth. Cause ofincrcastj 
of pressure. How should this principle affect the construction of acqueduct pipes, 
canals, &<:. 

14 




158 NATURAL PHILOSOPHY, 

&c. The lateral pressure being equal to the downward, it 
follows that the sides of a canal, or embankment, receive the 
greatest pressure nearest the bottom. 

427. The weight of a solid or cubic foot of water, is 1000 
ounces, or 62^ pounds. Now at the depth of 8 feet, as the 
pressure on a square foot is equal to a column of water 
whose base is 1 foot, and whose depth is 8 feet, the solid con- 
tents of such a column are 8 cubic feet. Therefore as one 
•solid foot of water is 62i pounds, and this number multiplied 
by 8 is 500, it follows that a column of water 8 feet deep, 
causes a pressure equal to 500 pounds ; at 16 feet the pres- 
sure is double, or equal to 1000 pounds, and so on in the 
same proportion. Thus at the depth of 64 feet, or eight 
times 8 feet, there is a pressure of 4000 pounds, which is as- 
certained by multiplying 500 by 8. 

428. From these facts we may form some idea of the vast 
pressure of the water of the ocean, which is supposed to be, 
in some places, four or five miles deep. The pressure at 
the depth of one mile is equal to the weight of 330,000 pounds. 
You may now understand a fact which has puzzled many 
people, viz. that in deep seas, it is impossible for the mariner 
to learn the exact depth by sounding, because the lead which 
is attached to the cord he uses, floats at a certain depth. 

429. A common square glass bottle containing only air, 
if corked and sunk in water to the depth of sixty feet, will be 
crushed inwards by the pressure. If the bottle is first filled 
with water, then corked, and let down to any depth into the 
sea, the bottle will not be broken, because the pressure of 
the liquid within, resists the external pressure. At a certain 
depth, the cork, owing to the compressibility of water, will be 
forced into the bottle, and this, in whatever direction the 
mouth of the bottle may point, whether downward, upward, 
or laterally ; for pressure, as has been already explained, is 
equal in all directions. 

430. The downward pressure of the particles of a fluid is 
occasioned by gravitation ; the lateral pressure results from 
the downward pressure pushing out at the side with equal 

\yeiglit cf a solid foot of water. Pressure of a column of water 8 feet deep. 
Ofa column 64 feet deep. Pressure of the Ocean. Why deep seas cannot be 
sounded. Glass bottle brolien by pressui'e. Cause of downward and lateral 
pressure. 



HYDROSTATICS. 159 

force the contiguous particles. For it must be remembered, 
that the fluid particles are not supposed to be piled exactly 

Fig. 120. above each other as at A, but to be arranged 
^ as at B. Tf the particles below had not a ten- 

;.}A B^^ dency upward,equal to the Aveight or downward 
pressure of the particles above, they could not support them. 
Their upward tendency may be considered as derived from 
the pressure around them. 

431. Even water itself, which was long supposed incapa- 
ble of being compressed into a smaller space, is found una- 
ble to resist the powerful pressure of its own element. An 
apparatus has been invented, consisting of a hollow brass 
cylinder, which being filled with water and closely slopped 
is sunk to a certain depth at which the stopper will be driven 
inwards. Means are contrived for ascertaining how far 
the stopper is driven in at different depths. The brass cyl- 
inder being full when it was closed, the stopper could not 
have been pressed inwards, unless some portion of the water 
within was expelled, or the whole compressed in bulk ; and 
since the cylinder allowed no portion to escape, it follows 
that the liquid was compressed, aad that this compression 
became greater at greater depths. 

432. The same experiments have been repeated with the 
. hydrostatic press. It has been proved, that under a weight 

of 1500 pounds to the square inch, water loses one 24th part 
of its bulk, and its specific gravity is increased in the same 
proportion. 

Level surfaces of Liquids. 

433. That liquids, when left free to arrange themselves 
according to their own laws, always maintain a horizontal 
position, is too familiar a fact to need any illustration. Yet 
though we speak of the level of the sea, it m.ust be recollect- 
ed that from the spherical form of the earth, the surface of 
the ocean Inust be curved. And however small any extent 
of surface may be, it is not, strictly speaking, exactly level. 
But from the size of the whole globe of the earth, the gene- 
ral curvature of those portions within the scope of our vision, 

Of upward pressure. Experiment for proving the pressure nnd compressi- 
bility of water. Experiment with the hydrostatic [iress. Curved surface of tlie 
Ocean, Why not perceptible. 



3 60 NATURAL PHILOSOPHY. 

is too small to afiect our sense of sight, or to alter the me* 
chanical laws of nature. 

434. From this tendency of liquids to settle into a level, 
arises the glossy smoothness of the calm lake and still foun= 
tain, which reflect the surrounding images as faithfully as 
the most perfect mirror. If these waters are disturbed, as 
soon as the exciting cause ceases, they again resume their 
smooth and equal surface. Water from highlands is contin- 
ually seeking to make its way downward, in order to find a 
level. Lakes and ponds in elevated countries are constantly 
pressing against their boundaries, and when these give way 
in the slightest degree, fearful inundations of the country 
below are the consequence. The beautiful valleys and pic- 
turesque glens, which we now behold, were probably once 
filled with water, which, in seeking its level, found some out- 
let of escape into a lower region. 

435. It is upon this level seeking principle in water, that 
aqueducts are constructed, as whether conveyed in artificial 
pipes, or natural channels, water will rise as high as its 
source. Suppose a reservoir of water A, to be on an eleva- 
tion at a little distance ft-om a city or village, this water may 




be brought in pipes or aqueducts through a valley, and then 
up an acclivity, until it reaches a height equal to that of the 
reservoir ; thus it may be distributed by communicating pipes 
to every street. 

436, The ancients, who were at great expense in the con- 
Mruction of aqueducts, often carried water over valleys by 
means oi aqueduct bridges, instead of conducting it through 

Tendency of water to. seek its level. Principle on which aqueducts ai'e con- 
structed. Aqueduct bridges of the ancients. 



SPECIFIC GRAVITY. 151 

pipes. For this reason some have supposed that they were 
ignorant of the law of hquids, which causes them to rise in 
pipes or channels as high as their source. But as they did, 
in some cases, use pipes laid in the earth for conducting wa- 
ter, it is probable that they adopted the more expensive 
mode of arcades, on account of their greater permanency. 
For, as the pressure in pipes is greater in proportion to the 
depth of the water below the reservoir, it follows, that in de- 
scending great declivities, the force of this pressure upon the 
pipes is so great as ultimately to burst the strongest material. 



LECTURE XXI 



SPECIFIC GRAVITY 



' 437. All bodies of equal bulk have not the same vv^eight. 
l4 piece of cork weighs less than a piece of hard wood of 
the same size, and a piece of lead of the same dimensions, 
weighs more than either. 

438. Thus each different kind of matter has its specific, 
or peculiar weight, which is expressed by the term specific 
gravity ; that is, the gravity o? species of things. 

439. The absolute gravity of any substance, is its real 
weight, or the force with which it presses downwards ; the 
relative gravity, or, which is the same thing, specific gravi- 
ty, is the weight of a substance, compared with others of 
equal bulk. It is owing to different degrees of density, 
that substances thus differ in regard to gravity. The more 
dense a body is, the more particles of matter are contained 
within a certain bulk, and the greater is its specific gravity. 
For example, lead is very a dense, and cork, a porous body. 

440. Children are sometimes puzzled by the question, 
which is the heavier, a pound of feathers or a pound of lead. 



Weiglit not depending on bulk. Meaning of the {Qnn specific gravity. Ab- 
solute and relative gravity. Cause of ditForence in gravity. A pound of feath- 
ers has the same absolute gravity as a pound of lead. 

14* 



j[62 NATURAL PHILOSOPHY. 

Now a pound of feathers has the same absolute weight, as a 
pound of lead, but the bulk of a pound's weight of the two 
articles would be very different, owing to the difference in 
their specific gravity. 

441. Water is the standard for estimating the relative or 
specific graviUj of solids and liquids. That is, if a certain bulk 
of any substance be found to ^have exactly the same weight 
as the same bulk of water, its specific gravity is called 1 ; if 
it be twice as heavy as the same bulk of water, its specific 
gravity is called 2, and so on. The specific gravity of gold 
is about 19 ; that is, gold is about 19 times heavier than 
water. 

But you v>^ill best understand this subject, by learning the 
method in which the specific g:avity of bodies is ascer- 
tained. 

442. Rule for ascertaining specific gravity. Weigh the 
body first in air, (that is, in the common raode,) then weigh 
it in water ; find how much weight it loses by being weighed 
\n water ; now divide the former weight by the loss sustained, 
and the result will be the specific gravity of the substance 
y/eighed, or its relative weight when compared with the 
weiofht of water. 

443. The figure represents an hy^ 
drostatic balance. Now suppose c 
to be a solid inch of gold suspended 
from the bottom of the scale h ; 1st, 
let its weight be ascertained, by put- 
'Z ting weights in the opposite scale, a, 
and suppose these to be 19 ounces; 
2d. place beneath the scale h, a tum- 
bler of water, the gold is buoyed up 
by the liquid with a force proportioned to the weight of the 
water which it displaces, and is found to lose one ounce in 
weight, or to weigh but 18 ounces. 3d. According to the 
rule already given, divide 19, the v/eight of the gold out of 
the water, by 1, the loss of weight sustained in the wa- 
ter, and the quotient is 19, v/hich is its specific gravity. 
That is, a piece of gold, weighing 19 ounces, occupies the 

Standard for estimating specific gravity. What is meant when the specific 
gravity of any substance is stated as 1, 2, &c. ? How may the specific gravity of 
a substance be ascertained? Hydrostatic balance. What is the first step in the 
process of finding the specific gravity of a substance 1 What the 2d step 1 
What is the 3d step? 



o* 




SPECIFIC GRAVITY, 163 

same space as a portion of water weighing one ounce, or, in 
other words, gold is 19 times heavier than water. 

444. It is found that this difference between the weight of 
the gold in air, and in water, gives the weight of a quantity 
of water equal to the bulk of the metal. This rule is founded 
on a law in Hydrostatics, that a solid body immersed in any 
liquid, not only weighs less than it does in air, btit that the 
diiference corresponds exactly to the weight of the liquid 
which it displaces ; and, it is evident, that the liquid thus 
displaced is of the same bulk as the solid, since the latter fills 
a space which before was exactly filled by the liquid. 

445. The heavier a body is, the less water will a given 
weight of it displace. Thus should you procure pieces of 
gold, silver, tin, and marble, each weighing one ounce, the 
ounce of gold would be the smallest of alhthe pieces, and the 
marble the largest; for the specific gravity of gold is 19, 
while that of marble is but 2 ; tin, though lighter than gold, 
is heavier than marble ; and silver is heavier than tin ; 
therefore the ounce of silver would be greater in bulk than 
the gold, and less than the tin : the ounce of tin would be 
larger than that of silver, and smaller than that of marble-, 

Pig- 123. ^ Take four tumblers of 

dotted, horizontal line ;' put the ounce of gold into the turn- 
bier D, that of silver into C, that of tin into B, and that of 
marble into A, you will find the water raised or displaced 
in proportion to the hulk, and not to the loeiglit of the sub- 
stances immersed. 

446. You will observe that whatever may be iheform of 
the different substances, their exact bulk, or size, is ascer^ 
tained by weighing them in water, as from the ease with 
which the liquid particles move, water accommodates itself 
to cavities and protuberances of all kinds. Thus it is that 
lumps of minerals of the most irregular forms, may be weigh- 

What quantity of water will weigh as much as the gold loses of ils weight in 
water ? How does it appear that the liquid displaced is of the same bulk as the 
sohd wliii-h has taken its place ? By what experiments can it be proved that the 
heavier a body is, the less»\vater will a given weight displace ? Bulk of irregu- 
lar masses ascertained by weighing them in water. 



164 NATURAL PHILOSOPHY. 

ed in water, and their specific gravities ascertained ; that is, 
their weight and bulk compared. By this means the mine- 
ralogist accurately distinguishes the various genera of mine^ 
xals, and depends on specific gravity, as one of his most 
valuable characteristics. 

447. ^ If all substances could be easily formed into regu- 
lar, solid figures, their comparative gravity could be deter, 
mined by simply weighing them in the usual manner ; thus 
a cubic inch of gold, weighing 19 ounces, a cubic inch of 
silver 10 1-2 ounces, and one of tin about 8 ounces, we 
could estimate their relative weight accordingly ; but 
most natural substances, such as diamonds and other pre- 
cious stones, and common mineralogical specimens, are of 
various and irregular figures ; it is therefore very important 
that there should be a method of estimating their exact bulk, 
and comparative weight. 

448. SjJeciJic gravity of solids lighter than water. 

The cases we have considered, are of such substances as 
are heavier than water, and therefore sink in it. 

When a body is lighter than water, its specific gravity is 
ascertained by attaching to it some heavier substance, which 
will cause it to sink, and the absolute w^eight and specific 
gravity of this additional substance being known, it is easy 
to find by subtracting from the loss of weight of the mixed 
mass in water, the loss of the heavy body, alone ; the dif. 
ference is the loss of the lighter body. 

449. Thus suppose that you wish to find the specific 
gravity of wood, which is lighter than water, and floats on its 
surface ; you know the specific gravity of copper to be 9, 
now suppose a lump of copper, weighing one pound, to be 
attached to a piece of wood. According to the method giv- 
en for ascertaining specific gravity, you have only to sub- 
tract from the weight of the whole mass in water, 9 for the 
loss of the copper, and the remainder of the loss of weight 
in water, is that of the wood, or lighter body ; which loss, 
being divided by the weight of the wood, out of the water, 
the specific gravity of the wood is ascertained. 



Advantage to the rnineralcgist. If substances were of regular foi-ms, how 
could their specific gravity be ascertained ? Most natural substances irregular 
in their forms. Mode of ascertaining the specific gravity of substances lighter 
than water. Experiment to prove the specific gravity of v/ood. 



SPECIFIC GRAVITY, 



l€o 



Specific Gravity of Liquids, 

iF'ig..l24. 

450. The specific gravity of liquids is ascer- 
tained by means of a simple instrument, called an 
hydrometer.^ This is a hollow, floating bulb of 
glass or metal, B, with a graduated tube, ad; the 
specific gravity of a liquid may be estimated, by 
the depth to which the hydrometer, when plunged 
into it, sinks, or by the weight required to sink the 
hydrometer to- a certain depth. Weights are sus- 
pended at C, for the purpose of sinking the instru- 
ment and keeping it in a vertical position. The 
weight necessary to sink the instrument to a certain 
mark on the tube, as o, determines the specific gra- 
vity of the liquid into which it is plunged. 

451. As the resistance of fluids, is in proportion to their 
density, it follows that the hydrometer will sink deepest in 
those fluids which are lightest. This instrument is used by 
brewers and distillers, to determine the strength of their li- 
quors. It is also used in salt manufactories, to test the 
strength of the brine. The deeper the hydrometer sinks in 
spirits, the better they are, because alcohol is specifically 
lighter than water, and the less the spirits are reduced with 
water, the lighter they are, and of course the less resistance 
they offer to the pressure of the instrument. In brine, on 
the contrary, the instrument is borne up in proportion to its 
strength, salt water being heavier than fresh water, in pro- 
portion to the degree of salt which it holds in solution. 

452. It is related, by Dr. Arnott, that a merchant of Chi- 
na, who had sold a quantity of distilled spirits to the purser 
of a ship, according to a sample shewn, went into his shop 
and added to each cask a quantity of water. The spirit 
being delivered on board the ship, was tested by the hydro- 
meter, and found to be reduced. The Chinese, ignorant of 
any human means by which the fraud could be detected, 
confidently denied it ; but on the exact quantity of water 
which had been added, being specified, he was seized with a 

* From the Greek words, udnr, waler, and met roii, measure. 



Hydrometer. Use of the hydrometer, 
hydrometer. 



Detection of fraud by moans of the 



166 NATURAL PHILOSOPHY. 

superstitious awe, and, confessing his roguen-^, offered to 
make ample restitution. When shewn the instrument by- 
means of which he had been detected, he was struck with 
admiration, and offered to purchase it at any price that might 
be demanded. 

453. There are many common facts, the pliilosophy of 
which can only be understood by a knowledge of the differ, 
ent specific gravities of bodies. When a person lies in a 
bath, he feels himself borne up by the liquid around him ; 
on going out of it, his Hmbs seem heavier than usual. The 
specific gravity of water, being greater than air, causes the 
difference in the sensations, on being surrounded by one or 
the other element. Water is said to have no weight in 
water ; thus a bucket in a well, rises with the smallest force 
until it reaches the surface of the water, after which its weight 
is sensibly felt ; many fishes are of nearl}' the same specific 
gravity as water, therefore when lying inactive they neither 
sink nor swim. It is said, that in former times, a certain 
king demanded of the learned men of his court, an explana- 
tion of the fact, that fishes had no weight in water ; many 
profound theories were offered, but none seemed satisfac- 
tory, kt length an unlearned man, consulting only the 
philosophy of common sense, balanced a vessel of water in 
scales, and on putting a fish into it, shewed that the weight 
in the vessel w^as increased by the whole weight of the fish. 
For supposing the fish to be of the same specific gravity as 
the water, that is as 1 to 1, it was the same thing, as if a 
certain portion of water had been added, which in its own 
element would lose no weight. 

454. Two columns of liquids of different specific gravities^ 
balance one another, ivhen their heights are inversely as their 
specific gravities. 



Why a person feels himself lighter in a bath. A bucket easily raised in wa- 
ter. Question of a certain king. Proposition. 





SPECIFIC GRAVITY. ' 167 

Pig. 125. In tlie bent tube A B, when the height of the col- 
umn B is as much higher than that of A. as the liquid 
B is lighter than the liquid A, the two columns will 
balance each other and remam at rest, at A and B. 
From the hydrostatic laws already considered, the 
the pupil will readily comprehend, that although 
the diameters of the colum.ns were different, this would 
not alter the rule now given, since the bases and 
heights of the columns of fluid, determine their force ; 
aiicTthis force must of course vary, with the specific gravi- 
ties of the liquids. Thus mercury having a specific gravity 
about 14 times greater than that of water, a column of mer- 
cury would balance a column of water 14 times higher than 
itself. 

455.. " A body lighter than its bulk of water, will 
loat ; and with a force proportioned to the differ- 
ence. Thus if the cylinder abed, be partly im- 
mersed in water, the upward pressure of the water 
on the bottom c d, is exactly what served to sup- 
port the water displaced by the body, viz. water of the bulk 
oi'efnd. The body therefore, that it may remain in the 
position here represented, must have exactly the weight of 
the water which the immersed part of it displaces ; and if it 
be lighter than this, it will rise higher, if heavier it will sink 
deeper."* 

456. The specific gravity of the human body is very 
nearlv the same as that of water, and when the lungs are fil- 
led with air, v/hich is lighter than water, the body will not 
sink. But in order to float upon the surface of water, it is 
necessary that a person should lie quietly with the face up- 
wards. By lifting up the head; as its weight in air is great- 
er than in water, a downward impulse is given ; and it is the 
same with respect to throwing the limbs out of water. Thus 
the struggles of one, who has accidentally fallen into deep 
v/aten-, tend to make him sink ; and the greater pressure of 
the liquid below the surface, compressing the air in the lungs, 
renders it more difficult for the body to rise. 

* Arnott. 

Exiiniile. Columnof mercury balancing a column of wcitor. Cause of bo- 
dies Hoaiing in water. Specific gravity of the human body. Cause of its sink 
ing in v/aler. 




168 NATURAL PHILOSOPHY. 

457. The figure represents a glass jar nearly filled with. 
Fig. 127. water, and covered closely with a piece of indiao 

rubber. The three figures are of glass, and be- 
ing hollow within and filled with air, are of less 
specific gravity than the water, so that they float 
on the surface. By pressing with the hand upon 
the elastic cover of the jar, a small portion of air 
which is between that and the surface of the water, 
is acted upon, and this pressure forces the water 
through cavities in the feet of the glass figures into 
their bodies, compressing the air within. This, 
increasing their specific g^-avity, causes them to sink. They 
do not sink to equal depths, because the cavity within the 
figure E, is greater than that within the figure D, and the 
same pressure will force more water into E than into D. 
For the same reason C does not sink as low as D. On rais- 
ing the hand, as the pressure is then removed from the air 
beneath the cover of the jar, the whole mass of water below 
is released from the pressure, and the elastic air within the 
figures expanding, drives out the water which had been for- 
ced inward, and the figures again rise to the surface. 

458. That bodies heavier than water sink in that jluid^ 
may seem to contradict the a^ssertion that upivard pressure is 
equal to downward pressure. But you must understand that 
weight and pressure do not mean exactly the same thing. 
Thus when a stone is thrown into water, following the im- 
pulse of gravity, it makes an attempt to descend ; but it can^ 
not do this without displacing as much of the water as is 
equal to its own bulk, therefore it is resisted, or pressed up- 
ward, by a force equal to as much water as is equal in mag- 
nitude to the bulk of the stone ; but the weight of the water 
is less than that of the stone, therefore the force pressing 
against it upwards, is less than its tendency downwards, and 
consequently, the pressure of the water being less than the 
weight of the stone, the latter will sink. 

459. You will sometimes see the specific gravity of a bo- 
dy stated in whole numbers and decimals, sometimes in frac- 
tions-only. — Now, as it is often important to be very accu- 



What causes the figures in the jar to sink? Wliy do they not sink to equal 
depths'? How can the figures be made to rise asain to the surfiice? Weight 
and pressure not synonymous. Wiiy does a stone sink in water .' 



SPECIFIC GRAVITY. 169 

'rate in ascertaining the specific gravity of substances, and as 
the numbers I, 2, 3, &c., would not in many instances ex- 
press this definitely, the weight of water may be considered 
not only as a unit, but as 10, 100, or 1000. Thus gold is 
a little more than 19 times heavier than water ; this may be 
expressed by a vulgar fraction, as 19^, or in decimals either 
as 19.25, or 19.250, the fraction 25 being one fourth of a hun- 
dred, and 250 being one fourth of a thousand, the same pro- 
portion is expressed in both statements. If the weight of 
water is estimated as a unit, then the specificgravity of gold, 
(which is nineteen times and a quarter heavier than water,) 
should be expressed as 19;^ ; if the weight of water is esti- 
mated as 100, then the specific gravity of gold should be sta- 
ted as 19.25, the decimal being the fraction of a hundred, 
&c. 

460. The specific gravity of pure alcohol is less than 
that of water ; it is estimated as 797 — that is, considering 
water as 1000. The specific gravity of milk is somewhat 
greater than that of water, it being 1.032. Platina is the 
heaviest of all known substances ; its specific gravity is 22, 
water being 1. The pure metals are the heaviest class of 

substances, their specific gravity being from 5 to 22. The 
metallic ores being a mixture of earth and other substances 
with the metals, are lighter than the pure metals, although 
usually above 4. The precious stones, as the diamond, em- 
erald, &c., have a specific gravity between 3 and 4. Com- 
mon minerals between 2 and 3. Some kinds of wood are a 
little heavier than water, as mahogan}^ which is 1,06 ; but 
generally wood is lighter than water. Cork has a specific 
gravity of 24. Hych'ogen gas, the lightest of all known sub- 
stances when compared to water, has a specific gravity of 
,00008, or eight one hundred-thousandths. 

Discovery of Specijic Gravity. 

461. Simple as appears tlie method of determining the spe- 
cificgravity of bodies, it was not known until about 250 years 

Modes of stating specific gravity. How is tlie specific gravity of golci ex- 
pressed .'' Specificgravity of Alcoliol. Of Milk. Of Platina. Of Metals ii> 
general. Of Metallic Ores. Of the precious stones and common minerals. Of 
Wood. Of Hvdrogen G:is. 



170 NATURAL PHILOSOPHY. 

before the Christian era. Archimedes, a philosopher of Si- 
cily, surpassed all his predecessors in depth of research into 
the principles of mechanics and hydrostatics. He is cele- 
brated for his treatises on mathematics, and for various phi- 
losophical discoveries arid inventions. It is recorded in his- 
tory, that Hiero, the king of Syracuse, having hired an ar- 
tist to make for him a crown of pure gold, suspected the man 
to have mixed with the gold given him for the purpose, some 
metal less valuable, but the crown weighed as much as the 
gold the king had famished, and he knew of no method of 
detecting the fraud, if there had been one^ and applid to Ar- 
chimedes for assistance. The object was, not to melt the 
crown in order to separate the mixed metals, if it were 
really composed of such, but to ascertain without injuring 
the workmanship, its quantity of alloy. It was a thing not 
to be ascertained by any rule then known, and the philoso- 
pher was much perplexed. At this time, upon stepping 
into a full bath, he observed that a quantity of water flowed 
over, which appeared equal to his own bulk, and that his 
w^eight seemed less in the water than out of it ; he was struck 
with the idea that '• a hody jjlunged into a liquid, loses a weight 
equal to that of a mass of the liquid of equal bulk,^' and leaping 
out of the bath, as it is said, he ran through the stieets 
shouting in the Greek language, '• em^eka ! eureka T^ ' I have 
found it out, I have found it out." On becoming more calm 
he proceeded to test the truth of his imagined discovery, 
and to apply it to the case under consideration. He took 
two masses, the one of gold, the other of silver, each of 
equal weight to the crown, and having filled a vessel with 
water, he first dipped into it the mass of silver, and accurate- 
ly determined the quantity of water v.'hich flowed out ; he 
tiien made a similar trial with the gold, and found that a less 
quantity had flowed out than before. Thus he estahhshed 
the fact, that the bulk of silver was greater than that of gold 
of the same weight. He then made the same experiment 
with the king's crov/n, and found that though its weight was 



Thue oftlie discovery ofspecific gravity. Suspicion of H'iero resj ecting liis 
crown. His applif-aiion to Aicliimedes. Tiie piiiN s..pher's perplexity, l^is 
obsenylion while baihing-. His expeiiiuents wiili pieces of gold and silver. 
With the king's crown. 



Liquids in motion. 171 

the same as the mass of silver and the mass of gold, it dis- 
placed less water than the silver, and more than the gold. 
Thus he ascertained that the crown was neither pure gold, 
nor pure silver. By determining the actual specific gravity 
of each he was enabled to ascertain the exact quantity of sil- 
ver which the artist had aded to the ji:old, to make the weight 
the same as the original weight of gold delivered by the 
king. 



LECTURE XXII 



OF LIQUIDS, IN MOTION, OR HYDRAULICS^ 

462. The term liydiraulics (from two Greek words udor^ 
water, and aulos, a pipe,) was at first used to signify the 
motion of water in certain musical pipes, in use among the 
Greeks ; it is now applied in a more general sense to liquids 
in motion; whWe hydrostatics, signifies liquids at rest. Bat 
ss it is not easy to preserve a distinction between the sub- 
jects, which properly belong to each of these branches of 
science, we shall not attempt to make a division, respecting 
which, writers on natural philosophy are by no means 
agreed. The popular use of the term hydraulics, is chiefly 
confined to the consideration of water-works, as pumps, 
fountains, engines, mills, and machines of various kinds, in 
which the power is derived from water in motion. 

463. Water can be set in motion by its own gravity ; 
as when it descends from a higher to a lower level ; in 
which case it will seek the lowest situation ; also by the 
pressure of condensed air, or by removing the pressure of 
the atmosphere, when it will rise above its natural level, and 
thus it may be forced to great heights. 

464. The velocity with which water spouts out at an ori- 



How was he able to ascertain tlie qnantity of silver added ? Definition of 
*7iydraulies. Popular use of the term, Causesoftha motion of water. Velocity 
of spouting fluids. 




172 NATURAL PHILOSOPHY. 

iice in the side or the bottom of a vessel, is as the square root 
of the orifice below the surface of the water. 

Fig. 123. 465. If at the distance ot'" one foot 

from the surface, the velocity is 1, be- 
cause 1 is the square root of 1 ; another 
orifice four feet from the surface would 
give the velocity of 2, because 2 is the 
square root of 4 ; and at 9 feet deep 
there would be a velocity of 3, because 
3 is the square root of 9. The figure 
represents a vessel discharging its con- 
tents at three orifices. The hquid from 
the upper spout being near the surflice receives but a slight 
pressure from the column above it ; and flows with a com- 
paratively slight velocity ; at the second spout, as there is 
a column of greater depth above it, the liquid is pressed out 
with greater velocit}^, and at the lowest spout, where the 
pressure is greatest the velocity will also be greatest. 

You will recollect that according to the principle which 
we have discussed, the force of the pressure does not de- 
pend at all upon the v/idth of the containing vessel, but upon 
the height of the column of fluid. 

466. In the preceding figure, the liquid projected from 
the side of the vessel describes the curve of a parabola: for. 
two forces act upon the body in motion, viz., the uniform 
pressure of the incumbent liquid, and the accelerated force 
of gravity. In investigating mechanical laws, we found 
that under these circumstances, moving bodies describe the 
curve of a parabola, and liquids here follow the same law as 
solids. 

467. The random or horizontal distance of the three 
spouts of v/ater, represented in the preceding figure, is= 
greatest at the middle spout, and equal above and below. 
The velocity of the lowest spout being greatest, we might 
suppose the random would be greatest, if we did not reflect 
that such a spout reaches the horizontal level, sooner than 
those which are higher. 



Velocity of spouting fluids at different distances from the surface. Why is the 
velocity greatest at the lowest spout, as represented in the figure? Why does 
the projected hquid describe the curve of a parabola .'' Where is the random 
greatest in the three spouts represented in the figure .'' 



LIQUIDS IN MOTION. 173 

468. . In drawing liquor from a cask, should three tubes 
be placed at different distances, viz., one near the top, one 
in the middle, and one near the bottom, and vessels of equal 
capacities be set under each spout, they would fill in the 
proportions we have already mentioned. The vessel under 
the lowest spout would fill most rapidly, and that under the 
spout nearest the top would fill the least rapidly, and the 
projectile force at each spout would decrease as the height of 
the column of liquid lessened. 

469. The velocity with which water issues from a spout 
is uniformly retarded as the surface of the column descends, 
and in this instance the mechanical law respecting liquids, 
is directly contrary to that of solid bodies falling freely by 
gravitation ; but it corresponds to the law respecting solid 
bodies thrown upwards. The cause of this difference in 
respect to the falling of liquids, projected from the side of a 
vessel, may be readily understood, since the force of projec- 
tion is greater, in proportion to the perpendicular height of 
the column, and this is constantly diminished by the flowing 
out of the liquid. 

470. The spaces described in equal times by the descend- 
ing surfice of the liquid column, are as the odd numbers, 
1, 3, 5, 7, i"), ike, luJizn hazkwards ; while in solid bodies 
fdliing freely by gravitation, the spaces described are as 
these numbers in their natural order. Suppose a vessel fil- 
led with water to be divided into 25 parts, and tubes opened 
for letting off the liquid ; if in one minute the surface descend 
through 9 of these parts, in the next minute it will descend 
through 7 parts, in the third minute 5, in the fourth 3, and 
in the fifth 1. 



Suppose the liquor from a cask to be at the same time running from three ori- 
fices at, diifereiit distances from tlie top ; which would discharti-e most rapidly I 
Would the projectile force be increased or diminished, as the column subsided 
jnheiglitl Velocity of spouting fluids uniformly retarded. Sjjaces described 
by the descending columns. 

15* 



174 



NATURAL PHILOSOPHY. 



Piff. 129. 

A 



11 



471. The Clepsydra, or water clock, is con- 

/ structed on this principle. If a cylindrical ves- 

'~ sel of water be found to discharge its contents 

in a given time, by an orifice at the bottom, 

the sides of the vessel being divided by lines 

— into equal spaces, these spaces become divisions 

of time. Thus if the vessel A empties itself in 

six hours, divide it into 36 equal parts — for the 

:3. first hour mark off 11 parts, for the second 

hour 9 parts, for the third hour 7 parts, for the 

^fourth hour 5 parts, for tlie fifth hour 8 parts. 

and for the sixth hoiir 1 part. 



472. There are some subjects, as the steam engine, pump, 
and the syphon, which might with propriety be considered 
under the head of hydraulics or liquids in motion ; but in 
order fully to comprehend the principles on which they are 
constructed, and on which their action depends, it is neces- 
sary to understand the nature and properties of air, and this 
carries us into the department of Pneumatics. 

473. Before entering upon a new subject, we will enu» 
merate some of the most important principles of hydro- 
statics. 

1st. Flydrostatics treats of the mechanical properties of 
now-elastic bodies, such as water. 

2d. Liquids press equally in all directions. 

3d. A column of liquid presses in proportion to its per- 
pendicular height, and the base of the vessel containing it, 
without any regard to the quantity. 



Clepsydra, or water clock. Subjects connected with hydraulics and pneu- 
matics. Synopsis of important principles in hydrostatics. 



LiaUlDS IN MOTION. 175 

4th. Specific gravity is the relative weight of equal bulks 
of different substances ; water being made the standard of 
comparison. 

5th, The science which teaches the laws of liquids in mo. 
tion is called liydrauhcs. 

6th. The velocity of spouting fluids, is as the square root 
of the depth of the orifice below the surface. 



PART IV, 



PNEUMATICS. 



LECTURE XXIIL 

AERIFORM BODIES, ATMOSPHERE, THE AIR PUMP. 

474. The Greeks under the term pneuma, included air, 
vapours, and gases of all kinds with which they were ac- 
quainted, and also the soul or spirit of man : from pneuma 
is derived 'pneumatics ; this, as a branch of natural philoso- 
phy, is that science which treats of the mechanical proper- 
ties of elastic or aeriform fluids. But it u chiefly of the 
phenomena of atmospheric air that this science treats, 

475. The pupil who has any acquaintance with chemis- 
try, knov\-s that there are in nature several kinds of gas ; that 
these by their union with each other form water and air ; 
and with metals form ores ; and which in various propor- 
tions, exist in all animal, vegetable, and mineral substances. 
But with gases, strictly so called, we have in natural philo- 
sophy little to do, because their part in the economy of na- 
ture is chiefly to be detected by the minute analyses, ana 
careful experiments of the chemist. 

476. The aeriform* bodies are vapours, atmospheric air, 
and gases : the former are not permanently elastic fluids, 
the latter are such. Vapours are elastic fluids, formed 
from liquid or solid bodies, by means of heat, and which, on 

*The term aerdform is from the Greek aer signifying air, or spirit. 

Definition of pneumatics. Gases. Aeriform bodies. Permanently elastic 
fluids and those wliich are not so. 



AERIFORM BODIES. 



17T 



losing heat, are condensed into a liquid or a solid state. Steam 
is vapour ; being nothing more than particles of water, 
which by the repulsive power of heat are driven to a greater 
distance, and thus become more rare and elastic. The 
same particles, by the loss of heat, may again exist in the 
form of water ; which, in its turn, by losing still more heat, 
may become ice. And, because steam may thus be conden- 
sed into a liquid and even a solid form, it is not considered 
as a permanently elastic fluid. 

4l11. The gases, and atmospheric air never exist in either 
a liquid or solid form, except when combined with other sub- 
stances, nor is it easy, by any ordinary degree of cold or of 
pressure, to bring them into these states. They are there- 
fore called permanently elastic fluids. 

478. A substance, to be elastic, must be compressible, 
and at the same time possess the power of expanding to its 
original bulk when the pressure is removed. " Let A B 
Fig. 130. be a cylinder, in which the piston P moves, 
air tight, and suppose that a small portion, as 
a cubic inch of atmospheric air in its common 
state, be contained between the piston and the 
bottom of the cylinder ; suppose the piston 
now drawn upwards, (as in the figure) so as 
to increase the space below it to two cubic 
inches. The air v/ill not continue to fill one 
cubic inch, leaving the other cubic inch un- 
occupied, as v/ould be the case if a solid or 
liquid had been beneath the piston in the first 
but it will expand or dilate until it spread itself 
through the two cubic inches, so that every part, however 
small, of this space, will be found occupied by air. Again, 
suppose the piston further elevated, (as at D,) so that the 
space below it shall amount to three cubic inches ; the air 
will still further expand, and will spread itself through every 
part of the increased space ; and the same effect would con- 
tinue to be produced, to whatever extent the space might be 
increased throi gh which the air is at liberty to circulate."* 




instance 



Lander's Treatise on Pneumatics. 



Different stale of the same particles. Why gases arc called permanently 
elastic fluids. Experiment to shew the elasticity of air. 



17^ NATURAL PHILOSOPHY. 

479. Atmospheric air is a perTuanently elastic fluid o.' 
gas, composed of two kinds of gas, oxygen and nitrogen. 
Tile ancients considered common air as a simple element ; 
but chemical analysis has shown its compound nature. 

480. As the mechanical laws and properties of liquids 
are, in hydrostatics, chiefly illustrated by a reference to wa- 
ter, as a representative of the whole class of non-elastic flu- 
ids, so the mechanical laws and properties of aeriform todies 
or elastic fluids are exemplified in 'pneumatics by a reference 
to common air. 

481. The solid portion of the globe, being most influen- 
ced by gravity and cohesive attraction, occupies the lowest 
place, forming the great centre of the whole mass. 

432. Above this, floating within cavities, and filling up 
the inequalities of the sohd substances, is the liquid bod}^ 
which constitutes oceans, seas, lakes and rivers. 

483. A third substance, less influenced by gravity, and 
not affected by cohesion, envelopes the whole, an atmospheric 
ocean of nearly fifty miles in depth. In this fluid, man and 
animals are fitted to exist, as the aquatic tribes are adapted 
to their watery element : fresh air is as necessary to the 
former, as water is to the latter. The fish does not die 
sooner when taken out of water, than does the bird or insect 
which is confined in a vessel exhausted of air. The fish, 
swims in the water by means of its fins, and the bird and the 
insect fly in the air by means of their vv^ings. Man by his 
muscular strength treads upon the sohd earth, but he moves 
in an ocean of air ; and every minute consumes not less 
than a gallon of this element.* There are plants v/hich grow 
only when surrounded and fed by water, but most of the 
vegetable tribes require the constant agency of air, in order 
to support their vital functions. Gentle currents of water 
bear upon their smooth surfaces, the light bodies which float 

* We here use the term element in its pyiular sense, and not according to the 
laws of science, which confine it to substances that are simple, or not capable of 
decomposition. 

Component parts of common air. Common air considered as representing 
tlie class ef aeriform bodies. Lowest portion of the globe. Substance which 
fillg up cavities of the earth. Substance which envelopes the globe. Atmos- 
pheric ocean. Its use and importance. Analogies between the aqueous and 
atmospheric oceans. 



AERIFORM BODIES. 179 

there, but the torrent luirries onvrard, carrying away rocks, 
and embankments, and destroying in a moment, works of 
art which required the labour of man for years in their con- 
struction. Air, which now gently wafts the floating gossa- 
mer, in the terrific form of the whirlwind uproots the oak 
of the lorest, prostrating alike the works of nature and of 
art. 

The Atmosphere. 

484. The Atmosphere which surrounds the globe consists 
of «z>, with the clouds and other vapours which float in it. It 
revolves v/ith the earth around the sun. It reflects the sun's 
rays upon the earth ; but it is proved that this power of re- 
flection, does not extend above the height of forty-five miles, 
therefore it is supposed that the atmosphere does not extend 
much beyond t'lat height above the earth. 

485. It is not of equal density in all its parts ; as the 
lower portions sustain the pressure of those above, they are 
consequently more dense. The greater the elevation, the 
tighter or more rare is the atn^sphere. 

486. The air is also colder in proportion, as we ascend 
into the higher regions ; for it is not heated by the rays of 
the sun which it transmits to the earth ; for gaseous fluids 
permit radiant matter freely to pass through them, withoul 
any absorption. Air receives heat from the earth, and by 
actual contact with such matter as contains it ; that is, the 
portion of air next the earth receives a portion of heat, a 
part of this is communicatexi to the next stratum of air, 
which in turn communicates heat to the air above it, and so 
on ; the quantity of heat communicated, decreasing in pro- 
portion as the distance from the earth increases. 'For eve- 
ry 300 feet of elevation, the temperature of the air is found 
to be one degree lower, that is, the cliniate is one degree 
colder. 

Air is Material, 

487. Matter is that which is perceived by our senses. 
We do not see the air which immediately surrounds us, be- 



Atinosi'liere, itsconiponeiit pans, vcvolnt ion and height. Its deiisily. Wiiy 
the air near the eanh is wannest. Proof tha* air is materia.'.. 



ISO NATURAL PHILOSOPHY. 

cause it is transparent, but we feel it when v/e move our 
hand rapidly back and forth, and we hear it in all the 
sounds which fall upon the ear. Its existence is also mani- 
fested to our senses in a great variety of common appearan- 
ces, and in experiments which may be almost infinitely mul- 
tiplied. Air, though generally considered as invisible, is not 
so ; we do not indeed see it in the apartment where we sit ; 
•but when we look abroad upon the concave firmament, illu- 
mined by light, we see an azure coloured vault. This 
colour is that of the mass of atmosphere through which we 
behold the celestial luminaries. The distant mountain and 
the ocean have the same hue, not because this is their own 
colour, but that of the medium through which they are seen. 
A small quantity of sea v/ater scarcely appears coloured ; 
but the deep sea has a decided green colour. These phe- 
nomena m.ay be easily explained ; a small portion of air or 
of sea water, reflects to the eye so little colour, as not to be 
perceptible, while large masses throw off colour in such 
Quantities, as to make an impression upon the eye. 

488. Extension and im'penetrahiU'y, have been stated to 
be the essential properties of matter* The extension of air 
is to be perceived on all sides, since we cannot draw a breath 
Vvithout its agenc5% and were we for a, few minutes to be de- 
prived of it, suffjcation and death must ensue. The im- 
peneirahilily of air, though this may seem at first doubtful, 
is not less cerfein, than that iron and wood possess the same 
property. That is, no other body ca,n exist in the same 
space which is occupied by air, anymore than one solid 
bod}' can occupy the same space which is filled by another 
^ohd bod}^ 

Fig. 131. 489. A very simple experiment, will 

^^ prove the impenetrability of air. Take 
a tumbler and plunge it perpendicularly 
into a vessel of water, and 3/0U vv^ill find 
that the liquid rises but a little into the in- 
verted tumbler, the air with which it was 
filled resisting the upward pressure. If 
instead of plunging the tumbler perpendi- 
cularly into the water, it is held a little 

' Tliou'jh the air is generally said to be transparent, it is only so when seen 
in small portions. 

Air not invisible. Extension a property of air. liDpenetrability of air. Ex- 
pei-iment to prove tlie impenetrability of air. 




ATMOSPHERE. 



181 



Ficr. 132. 




wclining, the air within will escape in large bubbles, and 
water will rise to fill the tumbler. 

The impenetrability of 
air may also be proved by 
the following experiment. 
Let A B be a glass vessel 
containing water to ,the 
level B, and let CD be a 
smaller vessel of the same 
kind empty, and having a 
short tube at the bottom furnished with a stop cock at F. 
Let a cork float on the surface of the water, at G, and let 
the vessel C D, having its stop cock closed, be inverted over 
ihe cork G, and let its mouth D, be pressed into the water 
in the reservoir A B. If the air in D were capable of per- 
mitting the entrance of another body into the space in which 
it is present, the water in the reservoir A B, would rise in 
the vessel C D, and stand at the same level in the latter as 
in the former. But the water does not enter the inverted 
vessel but at a very limited height, as vv^jjl be seen by the 
cork floating on the surface. The air which occupies the 
space C E excludes the water. This may be proved by 
opening the stop cock F, when the air which opposed the 
rise of the water will escape, and the water, by its upward 
pressure ascend to fill the vacant space. As air is com- 
pressible, the water rose in the vessel C D, to the height E, 
in consequence of the original bulk of the air which filled C 
D,',being reduced by pressure. 

There are many facts and principles difficult to be ex- 
plained in words, that may be illustrated by experiments. 
But as the necessary apparatus for making these experi- 
ments not always at hand, we shall endeavour to give 
plain and simple explanations, of the manner in vvhibh they 
are performed, and by means of figures enlist the eye in the 
"service of the understanding:. 



The Air-jmmp, 

490. One of the most important articles of a philosophi- 
cal apparatus, is the air-pump. By means of it, the pupil 



Use of experiments. 



16 



182 NATURAL PHILOSOPHY. 

sees the effect of the loss of air upon animals and vegetables | 
under the exhausted receiver, both die ; — he perceives too, 
that without air there can be no sound, for a bell under the 
exhausted receiver of an air-pump cannot be made to ring — 
he sees that a piece of lead and a feather, but for the resist. 
dnce of the air, would fall in the* same time from equal 
heights, or, that both are alike attracted by gravity — he sees 
that a very small portion of air in a bladder expands, when 
the pressure of air around it is removed, even to the bursting 
of the bladder which contains it ; — and that a shrivelled ap- 
ple under the exhausted receiver, by the expansion of the 
air contained within it, becomes plump and smooth. Now 
when these changes are actually presented to the senses, 
there is little danger that a pupil will torget their philoso=. 
phy, or have any doubts of the truth of the principles which 
they illustrate. 

We v/iil now define some terms v/hich will be used in ex- 
plaining the construction of the air-pump. 

491. 1st. Valve; this is merely a little door or lid, which 
permits a fluid to pass in one direction and prevents its re- 
turn. Examine a common bellows, and you will observe 
Fig. 133. on the lower board a large aperture, covered 
I? with m by a stiff piece of leather, commonly 
called the clapper. This covering, Vv'hich is 
movable on a hinge, is a valve, capable of 
being opened inwardly by the slightest pros- 
sure. On raising the upper board of the bellows, the cavity 
within is suddenly enlarged, and the valve is opened -by 
the pressure of the external air rushing in to fill the vacu- 
um. But the air cannot return by the same aperture ai 
which it entered, because it presses upon the valve and 
keeps it closed» On depressing the upper board of the bel- 
lows, a stream of condensed air rushes out at the only open- 
ing it can find, viz., the nozle. The reason why holes in 
the leathern sides of the bellows destroy its utility is nov/ 
apparent ; 'that is, the air finding other vent, issues but fee^ 
bly through the nozle. 

The valve of the air-pump usually consists of a strip of 

^•oiiiC of ilie , phenomena exliibited by t'le air-pump. Valve of a common bel- 
lows. How does the air enter and escape in a common bellows? Valve of ilie 
i,ir-pum/. 



m- 



AIR.PUMP, 



183 



oiled silk, tie J over a small orifice. The air by pressing 
outwards from the orifice raises this valve and escapes, 
while by pressing inwards it keeps the valve close to the 
orifice, and thereby allovv^s of no entrance in that direction. 



ig. 134. 



T 



4S2. Piston and cylinder ; — the piston is a 
stopper or movable plug, c, fitted to a hollow 
cylinder, d h, called a barrel. The piston is 
moved by means of a handle, a, called the pis- 
ton-rod. It is covered with leather, and oiled, 
so as to slide up and down the barrel, air-tight, 
or without allowing air to pass by its sides. 
Now, if in this piston there be no opening and 
the cyUnder be tight at the bottom, on pressing 
down the piston, the air which before occupied 

Uthe whole cylinder, will be' condensed into a 
bulk less than a hundredth part of its former 
magnitude. A valve in the piston may either 
admit or exclude the external air. If the valve opens upward, 
as at a in figure A, tlie air from below, at every downward 
movement of the piston escapes through it, v/hile none can 
follow to take its place in the cylinder. If the valve opens 
downwards, as at a in figure Ji, the air v/iil escape in that 
direction. 

Pig. 135. 493. Figure A represents the valve of an 

I 1 air-pump, in which the air is exhausted or 

3J — . pumped out ofa vessel called a receiver; and 
iigure B represents the valve ofa condenser, 
where a receiver is filled with condensed air, 
or has air forcibly crowded into it. The 
manner in which the receiver of the air-pump 
is connected with the cylinder and piston, we 
^^^^ will now explain. 



Describe the piston and cylinder. Piston-rod. How niav tbe air in acylin- 
<ier be condensed 1 Wiiat is the effect ofa valve in the \mU\\\ openiiiL;- upwards ? 
What, if the valve opens dovvnwards ? What does figure 135 ropre?oi!t ' 



184 



NATURAL PHILOSOPHY. 




494. You have here an interior section of 
an air-pump ; a, b are air-tight pistons work- 
ing each in its cyh'nder, c is the space undsr 
the receiver from which air is to be pump- 
ed ; d, a pinion-wheel and crank, which by 
its turning alternately, raises and deprissses 
the pistons ; e, a valve which when the piston 
h is raised, and a vacuum thus formed below, 
is forced upwards, and admits air from the 
receiver through the cavity c, this air rush- 
es out by opening a valve in the piston b ; 
/is a valve similar to e, and which, when 
the piston a is raised, admits the passage of 
a portion of air from the cavity c ; this air 
issues out of the air-pump by raisijg the piston valve at a. 

495. The figure repre- 
sents an air-pump, com- 
monly called a douhh- 
barrel air-pump, on ac- 
count of its two cylinders 
or barrels. The"^ use of 
two cylinders is merely to 
quicken the operation af 
pumping out the air ; for 
while the piston of one is 
rising, that of the other 
is falling. Each piston 
when elevated by the 
closure of the valve be- 
ef its ov/n valve, draws a portion 
A A are the brass cylinders in 



Figr. 137. 




low, and tne openui^ 
of air from the receiver 



which the pistons v/ork. C C are the toothed piston han- 
dles, adapted to corresponding teeth in the pinion-wheel. 
B is the crank by which the wheel is turned, and which in 
its motion alternately raises and depresses each piston, K 
is the bell-glass receiver from which the air is to be exhaust- 
ed. D E is the mahogany frame which supports the whole. 
I is a screw, by the turning of which, the external air is ad- 
mitted. H is a barometer connected with the receiver, for 
a purpose we shall hereafter explain. It is necessary that 



Interior section of an air-pump. Operation of the air-pump. 



AIR-PUMP. 185 

the reeeiver shall be so closely fitted to the brass plate of 
the air-pump on which it rests, as not to admit the entrance 
of any air. 

496. The philosophic poet, Dr. Darwin, thus describes 
the operation of the air-pump. 

" Now, as in brazen pumps the pistons move, 



The membrane valve sustains the weight above, 
Stroke follows stroke, the gelid vapour falls, 
And misty dew-drops dim the crystal walls; 
Rare and more lare expands the fluid thin, 
And silence dwells with vacancy within." 

497. The " vapour" and " dew drops" alluded to by the 
poet, are aqueous particles, of which the air usually con- 
tains a portion, and which are set free by the sudden expan- 
sion ofihe air in the receiver, causing a mist on its inner side. 
The allusion to silence, refers to the fact, that in" vacancy," 
or without air, there can be no sound. 

498. There is usually an appendage to the air-pump, 
which by means of a pipe communicating with the receiver, 
shews to what degree the air within is exhausted ; it is called 
the Mr oineler -gauge, (see H in the preceding figure of the 
air-pump,.) but v.'e must defer an explanation ot it, till we 
make you acquainted with the structure and uses of the ba- 
rometer. 

499. The air-pump is fitted for experiments, when the 
air is so exhausted from the receiver, that it ceases to force 
up the valves of the pistons. 

500. The object of philosophical experiments, is not 
merely to gratify curiosity, but to explain and illustrate the 
phenomena of nature ; and that young person who rests sat- 
isfied with an idle gaze, when witnessing such experiments, 
must he very stupid, or very frivolous. 

Darwin's desciiijtion of the air pump. Barometer gange. When is the air- 
[i!.im|i fitted for experimenis? Object of philosophical cxperin:ents. 

16* 



186 



NATURAL PHILOSOPHY. 



LECTURE XXIV 



PROPERTIES OF AIR. 



501. By means of the air-pump, certain properties of air 
are demonstrated ; these are, 1st. Weight ; 2d. Elasticity ; 
3d. Pressure, and 4th. Condensation. 



Piff. 1 



Weight of Air. 

502. 1. The air being exhausted from 
the receiver of an air-pump, it will be held 
fast by the pressure of the external air. 
On turning the screw which admits air into 
the receiver, it may be lifted up with ease, 
because the pressure of the air within, bal- 
ances that of the air without. 



503. 2. If a small receiver be placed 
under a larger, and both be exhausted, the 
larger vi'ill be held fast, while the smaller 
may be easily moved. This is because 
the large receiver having no air within, is 
weighed down by the external air, while the 
small one, having neither the pressure of air 
.without nor within, is moved with the' same 
'ease as if the pressure of air were balanced 
both without and within. 
504. 3. If a glass receiver, open at the top, be covered 
ti^ht with a piece of bladder, and then fixed upon the plate 
of the air-pump and exhausted of air, the bladder will burst 
with a loud noise. The weight of the air above, not being 
counteracted by any pressure below, produces this effect. 




Properties of air demonstrated by the air-pump. Ejiperimentsfor proving the 
weight of air. Exp. i. Exp. 2. Exp. 3. 



WEIGHT OF AIR. 1 87 

505. 4. A bottle uncorked, placed within a receiver, and 
exhausted of air, will be found to weigh less than when full 
of air. A wine quart of air is thas proved to weigh eigh- 
teen grains. 

508. The speafic graviti/ o^ air is about 800 times less 
than that of water. In explaining the construction and uses 
of the barometer, we shall have occasion to make some fur- 
ther remarks on the weight of air, especially of the whole 
atmospheric column. 

Elasticity of the Air. 

507. Air is 'perfectly elastic, since, when compressed, it 
tends to restore itself with a force equal to that by which it 
is compressed. A\v \s permanently c\diS{\c, because no force 
has yet been able to bring it into a liquid or solid form. 

508. The following experiments shew the elasticity of air. 
1. A bladder which seems empty, on being closely stop- 

ped at the neck, and placed under the receiver of an air- 
pump, wiii, when the receiver is exhausted, expand by the 
elasticit}^ of the small portion of air within. A very small 
quantity of air when released from external pressure will 
expand to an extent which appears almost unlimited ; on let- 
ting air into the receiver, the bladder thus distended, will 
shrink up again, and its sides be pressed together by the 
weight of the external air. 

509. 2. If a bladder with the neck tied, be put into a 
wooden box, with a weight of several pounds upon the lid, 
and this box be placed under a receiver, on exhausting the 
receiver, the air in the bladder will raise the lid of the box, 

"with the weight upon it, by its elastic spring. 

510. 13,: "The effect of air upon the lungs of animals, is 
exemplified by a simple instrument called the lungs-glass. 
This consists of a small glass vessel into which is screwed a 
brass tube, on the end of which is tied a small bladder. 
When this bladder is inserted in the glass vessel, it contains 
a small quantity of air, the inside of the bladder communi- 
cates with the atmosphere by means of the tube to which it 
is fastened. When the glass is placed under the receiver, 



Exp. 4. Specific gravity of'air. Air is perfectly and permaneiilhj elasti. . 
Experiments to shew the elasticity of air. Exp. 1. Exp. 2. Exp. 3. 



183 NATURAL PHILOSOPHY. 

Fig.^ 140. and the action ofthe pump commences, tlie air 
within the bladder will issue out at the tube, 
while that between the bladder and the glass, 
having no way of escape, will exert its elasti- 
city and press the bladder into a very small 
compass, (ts seen in the figure;) but on re- 
admitting the air into the receiver, part of it 
will enter the bladder and inflate it to its for- 
mer size. The same effect is produced upon 
the lungs of an animal when placed under a 
receiver, and the air exhausted — the air in 





the lungs is drawn out — the air in the cavity ofthe chest is 
thus expanded — the lungs are shrivelled up — their action 
ceases — and death is the certain consequence, unless the air 
be instantly admitted into the receiver, in which case the 
lungs are again inflated, and the animal breathes."* 

511. 4. A fresh egg contains at its large end a bubble of 
air ; if a small hole be made at the opposite end, and the 
egg be placed under a receiver, upon exhausting the air the 
contents of the eg-g will be forced out of the shell, by the 
elastic spring ofthe bubble of air within. 

512. The peculiar gurgling sound which takes place on 
decanting liquids, arises from the elastic pressure ofthe at- 
mosphere, which forces air into the interior of the bottle. 
At first, the bottle being filled vv^ith the liquid, no air can en- 
ter, but as soon as a portion of the liquid flows out, an empty 
space is formed within the bottle ; a bubble of air, forcing 
its way through the liquid in the neck, rushes to fill this va- 
cuum, and this causes the gurgling sound. This will con- 
tinue until such a portion ofthe liquid has passed out, as will 
allow the remainder to flow without completely filling the 
neck ofthe bottle, and thus permit a stream of air to pass 
in. The report which accompanies the' uncorking of bot- 
tles of beer, cider, and some kinds of wine, is owing to the 
elastic force of air which was condensed within the bottle. 
When liquor is bottled, a small space is left near the top of 
the bottle, this is filled with air ; on driving in the cork, this 

* Newtonian system of philosophy. 

The lungs-glass. Exp. 4. Cause of the sound in decanting liquids. In 
yneorking bottles of beer, &c. 



WEIGHT OF AIR. 189. 

sir is. condensed, the same quantity being made to occupy as 
much less space as the cork fills. 

The nature of some liquids is to produce, when bottled, a 
quantity of gas, and this often presses with such force as to 
drive out the cork, or if this is secured, to burst the bottle. 
The froth, which appears on pouring out bottled beer or 
porter, the effervescence of soda water, and the sparkling 
of cider and champaigne wine, are owing to the pressure of 
condensed air, which struggling to escape, appears in the 
form of little bubbles. 

Pressure of the Air. 

513. From the weight and elasticity of the air, arises its 
pressure ; and experiments which prove the tv/o former 
properties, equally demonstrate the latter. But for the sake 
of greater clearness, we prefer to consider these analogous 
properties under distinct heads. 

514. If, as we have already stated, one quart of air 
weighs eighteen grains, the weight of a column of air ex- 
tending nearly fifty miles above us, must be very great ; and 
consequently its pressure, which is in proportion to its height, 
must also be great. If the human body were subjected to 
the pressure of a column of air directly over it, without any 
counteracting pressure from within, and around, the incum- 
bent weight would be msupportable- 

Fig^i4i, 515. Let a glass vessel of the form here repre- 
sented, and having an opening at the top, be placed 
\^\ ^^^^ ^^® plate of the air-pump, and let a person 
lay his open hand upon the top of the vessel, so 
as to cover it closely ; on turning the handle of the pump 
a few times, the hand will be pressed down with such force 
as to render it impossible to raise it, and much pain will be 
felt. The pressure under the hand being removed by ex- 
hausting the air from within the glass, the pressure from 
above is thus left to operate without any counteracting force : 
the pain which is experienced will serve to shew in some 



Frothing cffiTvescence and snarliling ofliquors. What causes the pressure of 
air? How can the human body endin-c tlie downward jjrcssure of the air ? Ex- 
periment for proving the pressure orair. 




1.90 



NATURAL FHILOSOrKY. 




gree, what would be the effect upon the whole body, if all 
t the downward pressure were removed. 

^16^ The actual amount of pressure of a coI= 
umn of air upon every square inch, is demonstra- 
ted by an experiment with a simple apparatus 
called the Magdehurgh hemispheres.* This con. 
sists of two hollow hemispheres of brass A, B, 
) made to fit so closely as to form an air-tight 
globe. In the lower part C, are a stop-cock E, 
and a tube v/hich screws into the plate of the air- 
pump ; ^ when the air is exhausted within the 
;-lobe, the stop-cock being turned to prevent the 
return of the air, the apparatus may be taken from the air= 
pump, and the handle C is screwed on to the tube. Be. 
fore the air is exhausted from the interior of the globe, the 
two parts can be separated with ease, but when subjected 
only to external pressure, they adhere with a force which 
requires much power to overcome it. Under an exhausted 
receiver, the hemispheres thus exhausted may easily be 
separated, because the external pressure of air, as well a.-? 
ihe internal pressure, is removed. 

517. By m.eans of a steel- 
yard, hooked to a ring at the 
top of the globe, it may be. 
proved v/hat weight is neces- 
sary to overcome this pressure 
of the atmosphere, for when 
the weight W, is at a certain 
point on the arm of the steel- 
yard, the upper hemisphere is 
lilted up. Suppose the mouth 
of the hemisphere contains 12 square inches, and that it re- 
quires a weight of 180 pounds to raise the upper one ; if we 

* This experiment was one of the first Vi'liich drew the attention of m?inkind 
to the niechanic-i! properties ofnir. The inventor oftbe apparatus was Otto de 
Gaericl<e, of Mngdfbiir;(ii in Germany, who liad hemispheres made of a foot in 
diameter. It is said, that at a public exhibition ofliis a|)paratus, six horses of the 
Kmperor were unable to puil tlie hemispheres asnncer. There being no air- 
pump at lliis period, (about 1C57) the inventor was oblig-ed to exiiausi the hcrm's- 
pheres of air, by the slow process of filling thern with wjiter, and then extract- 
ing the water by means of an exhausting syringe, or common pump, applied ai 
the tube. 




PROPERTIES OF AIR. 



191 



Fig. 144. 



divide the weight, 180 by 12, the number of inches, the 
quotient is 15 pounds, which is the pressure on every square 
inch of surface. That is, a column of air reaching to the 
top of the atmosphere, and whose base is a square inch^ 
weighs 15 pounds. 

518. The figure represents a square 
inch ; the enclosed space must there= 
fore sustain the pressure of fifteen 
pounds. Every person must then 
sustain a pressure of air equal to 15 
times as many pounds as there are 
square inches on the surface of that 
body. Suppose the surface of a man's 
Lody to measure 2000 square inches, 
the force of the atmosphere pressing 

on that surface, would be equal to 30,000 pounds. But the 
air being sp uniformly distributed, within, without, and on all 
sides, we are not sensible of this pressure. 

519. Eoys, sometimes in sport, and 
without knowing it, make philosophical 
experiments ; thus the leather sucker, 
illustrates in a striking manner the 
pressure of air, arising from the joint 
effect of elasticity and weight. This is 
nothing more than a piece of leather 
having a cord attached to its centre. 

_^^g^j^ On moistening this, and applying its 
^^^ surface to any heavy body, as a stone 
or block of wood, it v/ill adhere so firmly that the body may 
be raised by the string. This effect arises from the exclu- 
Gion of the air between the leather and the stone. The air' 
pressing with a weight of nearly fifteen pounds upon a square 
inch, it follows that with a square inch of leather, a stone of 
nearly fifteen pounds weight may be raised. 

The power of .files, and some other insects, to walk on 
smooth ceilings with their feet upwards, or upon perpendicu^ 
lar panes of glass, depends on the same principle as the ac- 
tion of the sucker. Their feet are so constructed as to be 
capable of exhauslin^f; the air under tlicir soles. There is 




Amount of propsuro oVi ihe huiuau body. The k^t'ii', r surkcr 
oil ceilings aijd window- i)Laies. 



I'lilS WuiklRi.; 



Xg2 NATURAL PHILOSOPHY. 

an animal of the lizard kind, which can thus walk with its 
back downwards, and the walrus and seal walk up walls of 
smooth ice. 

520. " Breathing is, in part, the effect of the pressure and 
elasticity of air. When we draw in the breath, we first 
make an enlarged space in the chest. The pressure of the 
external atmosphere then forces air into this space so as to 
fill it. By muscular action, the lungs are next compressed 
so as to give to this air a greater elasticity than the pressure 
of the external atmosphere. By the force of this elasticity, 
it is propelled, and escapes by the mouth and nose. It is 
obvious, therefore, that the air enters the lungs, not by any 
direct act of these upon it, but by the weight of the atmos- 
phere forcing it into an empty space, and that it is expired 
by the action of the lungs in compressing it. The action 
of the com.mon bellows is precisely similar, except that the 
aperture at which the air is drawn in, is different from that 
at which it is expelled."* 

531. Casks containing liquids to be drawn out, and tea- 
pots, have in their upper parts, a small orifice for the admis- 
sion of air ; this is necessary, that the column of air pressing 
at the top of the cask, or the spout of the tea pot, may be 
counterbalanced by another atmospheric colnmn.; for the 
•liquid runs by its own weight, unless prevented by an oppo- 
sing pressure. 

A small hole in the lid of a tea kettle, wouM prevent the 
water, when boiling, from flowing out at the spout, which is 
caused by the force of steami within, overcoming the pres- 
•sure of the atmosphere acting on the water at the spout. V 

522. The figure represents an ink bottle, constructed 
^.pon the principle of atmospheric pressure ; as it presents 
Fig. 146. but a small surface of the fluid to the ac- 

j;;;^::^^^ tion of the air, the inconvenience of thick- 
ening and drying the ink, which attends ink 
I bottles with a large orifice, is prevented. 
•€c:sri i It ^"s evident that were the top, at A, open, . 

the liquid would flow out at the tube C, 
until it had reduced to its own level, that 

' Lnrdnei-s Treatise on Pneumntics. 

VVliiitetfect has air upon bretiihing 1 Why do caskc- and tea-pots have a vent 
hole. 



PROPERTIES OF AIR. 



193 



in the body A B. But this body is entirely close, while the 
tube C is open, and of sufficient depth for the immersion of 
the pen. The bottle is filled by being placed in an inclined 
position and pouring in ink at C. Let the bottle now be 
placed upright as in the figure, and the pressure of the at- 
mosphere at the orifice C, will prevent the liquid from run- 



Fiff. 147. 



In argand, or fountain 
lamps, the oil is in a part of 
the lamp, A, higher than the 
flame, and with its mouth 
downwards, but the mouth 
being immersed in oil, of 
which the surface C is near- 
ly on a level with the flame 
B, no oil can escape from 
above, but as the fiame con- 
sumes the free oil, which is 
its supply, and which is thus 
maintained at a constant uni- 
form elevation. 



523. The pressure of air is as the depth. As the bottom 
of a lake or sea supports the whole mass of water above it, 
so the part of the atmosphere next the earth, supports 
the whole mass of air. The lower portions of air sus- 
taining the pressure of those above, are therefore more 
dense. Air upon high mountains is, for the same reason, 
lighter than in lower situations. 

The fourth property of air, which we are to describe, is 
that of condensation, which will make the subject of our next 
lecture. 




Scientific ink bcUle. Fountain lamp. Pressure of air proportioned to its 
deptli. 



17 



194 



NATURAL PHILOSOPHY 



LECTURE XXV. 



THE CONDENSATION OF AIR. CONDENSING- SYRINGE. ARtI» 
FICIAL FOUNTAINS. AIR-GUN. DIVING-BELL. 



The Condensation of Air. 

524. Air, from its elastic properties, may be greatly con- 
densed, or forced by pressure, into a smaller space than that 
which it naturally occupies. The simple experiment previ- 
ously named, of plunging an inverted tumbler into water, 
shows into what a small space a tumbler full of air may be 
forced. 

525. The spring, or elasticity of condensed air, is equal to 
the force which compresses it. 

Fig. 143. • 526. Various 

experiments may 
be made with a 
machine called a 
condenser. At A? 
is a brass barrel 
containing a piston 
with a valve open- 
ing downwards. — ■ 
On raising the han- 
dle {a) of the pis- 
ton, the air presses 
through the valve, 
and is forced thro' 
a tube communica- 
ting with the recei= 
ver B ; at every 
stroke of the piston 
more air is thrown 
into the receiver, 
which, in order to 




What experiment shows t!ie ro-nleusatioa of air 7 To what is tiie elasticity 
of condensed air etiuaH Condenstr. 



CONDENSATION OF AIR. 195 

vsustain the internal pressure, must be made of very thick 
and strong glass. The receiver is held down upon the plate 
C, by the cross piece D, and by the screws F E. The 
stop cock G, is for the purpose of letting out the condensed 
air. 

527. You will perceive that the operation of this machine 
is the reverse of that of the air-pump; in the latter case, we 
pump air out of the receiver ; and in the former, we press 
air in. By means of the air-pump, we cause air to expand 
and become more and more rare ; by means of the conden- 
ser we continually add to its density. The receiver of a 
condenser may be compared to a wool sack, at first filled 
with wool lying loosely, as in its natural state, and then 
crowded with successive portions, until it is made to contain 
a weight many times greater than at first. But compressi- 
ble as wool is, it is far less so than air, which can he lessen- 
ed in hulk to a degree to which no limits can he assigiied hut 
the want oj strength in the apparatus used, and of force in the 
poioer applied. 

628. With the receiver of the condenser, when properly 
prepared, a variety of interesting experiments may be ex- 
hibited. 

1. A bell emits a much heavier sound when rung in air 
condensed, than in common air. 

2. A thin bottle containing common air, and closely cork- 
ed, is broken inwards by the pressure of condensed air. 

529. A condensing syringe, is a simple instrument used 
for the condensation of air. It is constructed on the same 
Fig. 149. principle as the 

common syringe, 
with which children 
amuse themselves 
in throwing water 
to a distance. A 
strong rod of elder 
having the pith taken out, furnishes the hollow cylinder A 
B, and a plug of solid wood C, is the piston ; D, is the piston- 
rod. On dipping the end of this syringe into water, and 



Comparison between the air-pump and condenser. To what is the receiver 
of a condenser compared 1 Experiments with condensed air. Condensing 
syringe. 




196 NATURAL PHILOSOPHY. 

drawing up the handle of the piston, the air is torced out- 
ward, and water rushes into the cylinder to supply its piace. 
When the piston is pressed down, the water is forced out, 
and may thus be thrown to some distance. In the conden- 
sing syringe, instead of a solid piston, there is a valve which 
opens downward, and by this means, air may be pressed into 
a receiver, but cannot pass in the contrary direction. Or 
the piston may be solid, and the condensed air be forced 
through a tube of the cylinder into a receiver. 

530. The power of condensed air may be shewn in the 
production of artificial fountains. Let a strong vessel of 
brass or copper, be furnished with a stop cock, inserted at 
the top, from which a tube proceeds nearly to the bottom. 

Fig. 150. Let the vessel be partly filled with water, 
mm and with a condensing syringe fitted to the 

'Hftlli upper part of the tube, introduce an extra 

quantity of air into the vessel. This air is 
forced below the surface of the water 
through the tube which extends to the low- 
er part of the vessel, and the stop cock is 
then shut. Being now under strong pres- 
sure, the tendency of the air is to expand 
to its natural bulk, therefore the syringe 
is unscrewed, and the stop cock turned, so 
as to admit a passage upward ; the conden- 
sed air acting on the water above, forces it 
through the pipe, and thus produces a beau- 
^SA tifulje^ (Teau.'^ The more dense the air is 
made within this fountain, the greater will be the height to 
which the water is forced, because the elastic power of air 
is in proportion to the force which compresses it. If a vessel 
of similar construction to that represented in the figure, and 
containing common air, be placed under the tall receiver of 
of an air-pump, when the surrounding air is rarefied, the 
jet will arise as in the case of condensing the air within. 

531. The Geysers of Icelan-d, are spouting springs, oc- 
casioned by the force of confined air, or gas, acting upon 
the water ; this force is immense, since not only water, but 

* A Prencli phrase signifying an upward spout of water. 
Artificial fountains. The Geysers. 



ii niiiiiiii",iaii;iH i'i"ii!iini !iii'!iiiiii ii 



CONDENSATION OP AIR. |97 

large stones are thrown by it, to the height of more than two 
hundred feet. 

532. The air-gun, affords a striking proof of the force of 
condensed air. This, in its general appearance, is very like a 
Fig. 15L 




connmon gun, with the addition of a metallic ball, A ; into this 
ball, which is furnished with a valve opening inwards, the 
condensed air is forced by means of the syringe, after which 
the ball is screwed on to the gun, below the lock, as appears 
in the figure. The gun is now loaded with a bullet, and the 
lock beinty sprung, acts upon a pin which opens a valve ; 
the condensed air now rushes into the barrel of the gun, and 
by its sudden expansion, forces out the bullet. 

533. The diving-bell exhibits an interesting illustration of 
the compressibility, elasticity, and impenetrability of air 

534. When an inverted tumbler is plunged into water, 
the liquid does not rise to fill the vessel, but the air with 
which it v^as before filled, becoming more dense by pres- 
sure, remains, and occupies a certain space ; this space is as 
impenetrable to water as if it were filled with so much lead. 
The diving-bell, which is a large, open mouthed vessel, ca- 
pable of containing one or more persons, is letdown into the 
water, which (according to the laws we have stated respect- 
ing the properties of air,) will only rise to a certain height 
in the bell. 

535. By means of this machine, men are able to descend 
to considerable depths in the ocean, for the purpose of sa- 
ving valuables from the wrecks of vessels, and of pursuing 
works of submarine architecture, such as laying the foun- 
dation for harbours and lighthouses. The diving-bell is 
also used in pearl and coral fisheries. 

Air-gun. What properties of air are illustrated by t!ie diving-bell. "^ M-'liy 
does nut water completely fill the diving bell ? The uses of the diving-bel!. 

17* 



198 



NATURAL PHILOSOPHY. 




536. When first introdu- 
ced into use, it was made of 
copper, and constructed in the 
form of a bell, as in the fig- 
ure, the height being about 
eight feet, and the diameter of 
the bottom five feet^ and that 
of the top three feet; it con- 
tained about eight hogsheads. 
Light was admitted by strong 
spherical glasses, fixed in at 
the top, as in the cabins of 
vessels. An English poet, 
says, 



" Lo ! Britain's sons shall guide 

Huge sea-balloons beneath the tossing tide; 

The diving castles, roof'd with spheric glass 

Ribb'd with strong oak, and barr'd with bolts of brass 



537. When the diving-bell is first let down into the wa- 
ter, it is full of air, but the pressure of the surrounding wa- 
ter, (which pressure increases with the depth,) acting upon 
the enclosed elastic air, compresses its bulk, and the liquid 
rises proportionally in the bell. 

538. As a column of water 34 feet deep,, causes a pres- 
sure equal to a whole column of the atmosphere, it follows that 
at this depth, (that is, 34 feet,) the air in the bell is under a 
pressure equal to two atmospheres, viz. ; that of the whole 
atmospheric column and the column of thirty -four feet of 
water ; the air is therefore here condensed into half its ori- 
ginal bulk. As the depth of water, and consequently the 
pressure increases, the air will be proportionally condensed, 
and the water will rise in the bell. 

539. When the bell is half full of water, the air is twice 
as dense as in its ordinary state at the surface of the earth, 
and the diver at each inspiration of the breath, will receive 
twice as much air into the lungs, as when breathing at the 
siirface of the earth. 



Its construction. 
of thirty-four feet. 



What condenses the air in the bell ? Pressure at the depth 
Wlien is the air twice as dense as common air .'' 



CONDENSATION CF AIR. 



199 



540. In breathing, the diver is constantly throwing from 
his lungs a large portion of gas, which is fatal to animal 
life.* This impure air being more rarefied than the air 
within the bell, rises, and is let off by opening a stop cock at 
the top of the machine. In order to supply the diver with 
fresh air, barrels of air having leaden weights attached to 
them are let down, (see c in the preceding figure,) and by 
means of connecting tubes convey the air into the bell. 
At e (see preceding figure) is a man walking at a little dis- 
tance from the bell, to recover some bales of goods which 
had been thrown overboard from a vessel in distress. He 
wears on his head a leaden cap, having glasses in front to 
admit light, and breathes by means of air from the flexible 
tube connected with the bell. In this manner the divers 
sometimes go a hundred yards from their bell. 
_ The bell is furnished with seats for the workmen, and 
with tools of various kinds. 

^ ^g- '^3- 641. The bell above described, is at 

present less in use than a machine of 

later construction, which is considered as 
%^ an improvement, (see the figure.) «, 
is a bent tube connected v/ith a forcing 
air-pump d^ by means of which a con- 
stant supply of fresh air is sent down 
from a ship above, and which the diver 
can obtain by turning the stop cock. 
At the bottom are heavy balls of lead, 
in order to sink the bell vertically. Men 
in tlie ship above, raise the bell by means 
of ropes and fixed pullies. Signals are 
made by the divers to those above in 
in various ways, by means of ropes con= 
nected with the ship. When they wish 
to be drawn up, they pull a rope 
which rings a bell ; when they want -to 
convey information to those above, they 
k write upon a sheet of lead and send it 




Carbonic acid <fas. 



What renders the air in the hell impure'? Ilovv is the impure air let off? 
How is the diver supplied with fresh air ? Describe the diving-bdl reprcseuled 
in figure 153. 



200 NATURAL PHILOSOPHY. 

lip, by pulling a cord, moving over a pulley fixed to the 
ship. 

We have been thus particular in describing this machine, 
b(^cause it is a remarkable application of the principles of 
;pneumatics, and illustrates the properties of air in a manner 
at once strikini^ and familiar. 



LECTURE XXYI. 

BAROMETER. EFFECT OF HEAT UPON AIKo 

542. The ancients had no conception that the pressure 
of air caused it to penetrate every crevice and cavity, on 
the surface of the earth ; they said therefore, it was be^ 
cause nature abhorred a vacuum, (or empty space,) that 
where there was nothing else, there was sure to be air. 

543. They perceived that when a solid or liquid was by 
any means removed, the surrounding air immediately rushed 
in to take its place, but instead of referring this fact to the 
simple and obvious principle of atmospheric pressure, they 
seemed resolutely to shut their eyes to the light of truth, 
and rested satisfied with their absurd hypothesis. The ef^ 
feet of suction with the mouth, is probably one of the first 
ways in which the subject of atmospheric pressure forced 
itself upon the observation of mankind. When one end of 
a tube was immersed in a liquid, and the other placed in the 
mouth, the air was withdrawn from the tube by inhaling, 
and the water rushed into the tube as fast as the air left it. 
Now ancient philosophers could not see in this any evidence 
of atmospheric pressure, but like children, who attempt 
to account for what they do not understand, they said, 
" we suppose this takes place because nature being uneasy 
with a vacuum, makes the water rise to fill it." This kind 
of reasoning, though fatal to the progress of true physical 
science, did not prevent men from constructing common 

Ignorance of the ancients respecting atmospheric pressure. Their h3'pothesis. 



BAROMETER. 201 

pumps of various kinds, so that they answered the desired 
purposes. But nearly two hundred years ago, as sonne en- 
gineers of the Grand Duke of Florence attempted to raise 
water, by means of a common pump, to the height of fifty or 
sixty feet, they perceived that the water after mounthig about 
thirty-four teet, would rise no higher. They communicated 
this fact to Galileo, the most celebrated philosopher of that 
day. After various experiments, he became satisfied that 
this was an universal law of nature, and that the rise of wa- 
ter to a certain height in pumps exhausted of air, was nei- 
ther owing to nature's horror of a vacuiun, nor to the power 
of suction, (as some had vaguely suggested,) but to atmos- 
pheric pressure. 

644. Torricelli, a pupil of Galileo, carried his enqtiiries 
farther. As a column of thirty-four feet of water, is equi- 
valent to a column of air extending upward from the surface 
of the earth, through the whole region of the atmosphere, 
why, he enquired, may not a column of any other fluid, of a 
given height, balance a column of air. As quicksilver was 
nearly fourteen times heavier than water, he imagined that 
a column of that fluid, of one fourteenth part the height of 
a column of water thirty-four feet high, might be equal to 
the pressure of air. He therefore filled with quicksilver, a 
Fig. 15^. glass tube, A B, of about three feet in length, closed 
at one end and open at the other, and placing the 
open end of the tube in a basin of quicksilver, C, 
found that the fluid in the tube fell a little, but re- 
mained suspended at about 29 or thirty inches, leav- 
ing a space at the top of the tube above the quick- 
silver, which was a perfect void or vacuum. By di- 
• Jviding 34 feet, or 408 inches, (the height of water 
[||| which the pressure of the atmosphere will support,) 
by 14, (because quicksilver is 14 times heavier than 
water,) the quotient 29, shews that a column of quicksilver 
of the height of 29 inches, equals in weight a column of wa- 
ter of 34 feet. 

545, But even after the experiments of Torricelli, though 
it was admitted that the quicksilver was suspended in the 

Attempts to raise water in pumps mote tlian lliiily-lonr feot. Discovery of 
Galileo. Tonicclli'd experiments. What chIluuh of wr.Wr and wliat of quicksii- 
ver, are eqn;il in weight to a column of tlic atuiosi.hcre i* \V iuit fact respecting 
litmusphcric pressure was still unobserved 1 



202 



NATURAL PHILOSOPHY, 



tube by the pressure of the surrounding air, it was not ob- 
served that the height of the colunnn of quicksilver was not 
always the sanae ; or in other M^crds, the fact was not yet 
known, that the 'pressure of the air was at sometimes greater 
than at other times, 

546. Butas Torricelli's tube excited the attention of men of 
science, it was soon discovered that the quicksilver did not al- 
ways stand at the same height, and moreover that its rising, or 
falling, was usually accompanied or followed by a change of 
weather. The quicksilver being found to vary from about 27 
to 31 inches, a graduated scale was affixed to the tube, 
divided into inches and tenths of an inch, in order to show with 
accuracy, these variations ; this instrument was called the 
weather-glass, and afterwards received the more scientific 
name of barometer. 

Fig. 155. 547. The word barometer, is from two 

Greek words, baros, weight, and metron, 
measure, signifying to weigh the atmos- 
phere. Let a tul>e. A, of nearly three feet 
in length, closed at one end and open at the 
other, be filled with quicksilver and then 
inverted in a cup, B, also containing quick- 
silver. Now if the tube were open at the 
top, according to the law that all fluids 
seek an equilibrium, the quicksilver from 
the tube v/ould descend to a level with that 
in the cup. But at the top of the column 
of quicksilver there is no pressure, because, 
v»'hen the tube v/as filled with this fluid, all 
the air was pressed out, and when on in- 
verting the tube, a space was left at the top 
by the descending of the quicksilver, this 
space was a perfect vacuum, and therefore 
all downward pressure upon the column of 
fluid in the tube, is removed. But the air 
presses upon the quicksilver in the cup, and 
this forces the fluid upwards, or which is 
the same thing, supports it thus suspended, 
with the open end immersed in the contents 



Main' 



How was the variation in atmospheric pressure discovered? The weather- 
glass. Meaning of the word barometer. Constrnction of the barometer. Why 
doesnot the quicksilver in the tube of the barometer run into the cupl 




BAROMETER. 203 

of the cup. And this column of quicksilver mu^st have the 
same weight as a column of the atmosphere of the same 
base, or it would not be thus balanced by it. 

Fig. 156. 

p> 548. As the column of quicksilver varies 

J L in height through a space of two or three inch- 

■^ es it follows that a given column of air does not 

always exert the same pressure, or in other 
words, does not always weigh the same. Ba- 
rometers are sometimes made with the lower 
end of the tube bent, as in the figure, and an 
open cup at the lower part containing mercury. 
The principle of its construction and operation, 
is the same as in the barometer with the straight 
^^ tube. 

549. In describing the air-pump, we remarked, that with 
it, was usually connected a part called the harometer-gauge» 
The object of this is to measure the degree to which the air 
is rarefied. When the exhaustion of the air in the receiver 
begins, the quicksilver of the barometer falls, because the 
air which supports it is lighter. If it fall a thousand parts 
below where it stood before the action of the air-pump be- 
gan, the air in the receiver is said to be rarefied 1000 times. 

Uses of the Barometer. 

550. 1. The barometer enables us to determine the ex- 
act weight of a column of atmospheric air, since this is equal 
to the weight of a cylinder of quicksilver thirty inches in 
length. 

551. 2. It is used for the purposes of determining the 
height of mountains, ascent of balloons, &c. ; as atmospher- 
ic pressure is less in proportion to elevation, the barometer 
falls in the same ratio. The common rule is, that the ba- 
rometer falls one inch for a thousand feet of elevation. Thus 
in ascending a mountain, we should infer from the fall of the 
quicksilver, half an inch, that we were five hundred feet 

What proves that the column of quicksilviM- in llio hnronu'tn- has the same 
weightas a cohimn of air.'' What does lh(> vaii:iiiiii) in th;- i'.ironicter prove? 
Barometer coiiiiected with the air-puni|i. ILMiiht of an alniospheric cohuiin dc- 
• nniiicd by the barometer. Ellcct of elevation upon tlic baromitcr. 



204 NATURAL PHILOSOPHY. 

above the level of the sea. Upon the summit of Mont 
Blanc, an elevation of fifteen thousand feet, the barometei 
falls about fifteen inches. 

55'2. 3. The barometer is of great use to the mariner, 
who in unknown climates, is often able by its variations, to 
foresee and prepare for sudden changes of weather. " The 
watchful captain of the present day, trusting to this extraor- 
dinary monitor, is frequently enabled to take in sail, and to 
make ready for the s.orm, when in former times, the dread- 
ful visitation would have fallen upon him unawares."* 

553. 4. The sudden fall of the miercury in the barome- 
ter generally denotes rain or wind, or what v\^e call bad 
weather. Though, in such weather, we complain of the 
heaviness of the air, it is, in fact, its lightness, that causes 
the feelings of dullness and oppression which we experience. 
For at each inspiration of the breath, we take in less air 
when it is rarefied than when it is more dense ; on the con- 
trary, as we have before remarked, the man in the diving- 
bell at the depth of thirty-four feet of water, where the pres- 
sure is that of two atmospheres, breathes air of twice the 
usual density. When the air is more light or rare than usual, 
the damp vapours and unhealthy gases, which, supported by 
pressure from below, floated in higher regions, now descend 
towards the earth. These vapours and gases have an unfa- 
vourable influence on the human S3^stem, obstructing perspi- 
ration, the free play of the lungs, and the circulation of the 
blood, and in this way give rise to diseases of various kinds. 
When therefore you see fog hanging over the surface of the 
earth, and smoke falling instead of rising, you may, without 
consulting the barometer, safely infer that the surrounding 
air is lighter than when fog and smoke rise into higher re- 
gions of the atmospliere. 

554. As the falling of the barometer denotes bad weather, 
so its rising announces fair weather, though these indications 
are not always to be depended on, especially when the va- 
riations in the height of the mercury are slow and inconsid- 

' Arnott's Elements of Physics. 



Use of the bnrometer to the mariner. What is indicated b)' the sudden fall of 
the barometer .'' Air lighter in bad Tv-e.ither. Effect of a light atmosphere upon 
itte human svstem. What is indicated bs" the rising of the barometer ? 



BAROMETER. 205 

Arable. It is stated by English writers, that on the occa- 
sion of the great Lisbon earthquake, the barometer, even at 
the distance of Great Britain, fell five or six inches ; a phe- 
nomenon v/hich is scarcely ever observed to take place, at 
the surface of the earth, under any circumstances. 

The mean height of the Barometer, • 

555. The mean pressure of the atmosphere at the level 
of the sea, is proved to be nearly the same in all parts of 
the earth. The mean height of the mercury in the barome- 
ter, has been found to be about 30 inches, in various places 
in the torrid, temperate and frigid zones. 

556. [n making accurate o})servations with the barome- 
ter, it is necessary to have attached to this instrument, a 
thermometer, with a scale of correction to shew how much to 
add or subtract from the height of the mercury, on account 
of changes of the temperature. The mercury being made 
lighter by heat, will rise in the barometer tube, even 
when no change has taken place in the pressure of the air. 
The thermometer shews exactly the degree of this expan- 
sion of the mercury by heat, and therefore what must be 
subtracted from the height of the barometer, in calculating 
upon the weight and pressure of the atmosphere. On the 
contrary, in cold weather the mercury is heavier, and con-- 
sequently will stand lower in the barometer, although the 
pressure of the air may be the same ; something therefore 
must then be added to the report of the barometer. At the 
equator we should have to subtract from the height of the 
barometer, while in the frigid zone we should add to it ; and 
this, according, to the degrees of temperature indicated by 
the thermometer.* 

* For a description of the thermometer, let the pupil refer to " Chemistry for 
Beginners." 2d. Edition, page 41. 



Fall of the barometer at the time of the Lisbon earlhquuke. IMean pressure 
of the atmosphere at the level of the sea. Use of eonuecting the tlierraumetoi 
v/illi the barometer. Elfect of temperature upon the barometer, 
IS 



206 . NATURAL PHILOSaPHYc 



Effect of Heat vpon Air. 

557. Heat, which so much affects solids and liquids, has 
a powerful influence upon air. Of this we are continually- 
reminded by the changes of temperature around us; thus we 
say, the air is chilly, or warm, hot, or cold. But as the 
moisture or dryness, the stilhiess or motion of the air all con= 
duce to these variations of temperature, we are not to attri- 
bute them to heat only. 

558. Heat expands air, and tiius rarefies, or makes it 
lighter. Let a bladder, tied at the neck, and containing 
a small quantity of air, be held near the fire, the sides will 
soon begin to be pressed out by the expansion of the air 
within. On removing the bladder to a colder place the air 
will condense, and its sides collapse as before. 

559. The balloons^' first used were filled with hot air^ 
which, being lighter than the atmosphere around, arose and 
floated in it. Dr. Arnott says, '' the first balloon was con- 
structed by a man itinerant of v/hat he was really effecting. 
Seeing the clouds float high in the atmosphere, he thought 
that if he could make a cloud, and enclose it in a bag, it 
might rise and carry him with it. Then erroneously deem= 
ing smoke and a cloud the same, he made a fire of green 
wood, wool, &;c., and placed a great bag over it, with the 
mouth downwards to receive the smoke. He soon had the 
joy to see the bag full, and ascending ; but he understood 
not that the cause was the hot and dilated air within, which 
being lighter than the surrounding air, was buoyed up, while 
the visible part of the smoke, which chiefly engaged his at- 
tention, was really heavier than the air, and was an impedi- 
ment to his wishes." 

560. The two Montgolfiers, in France, may be considered 
as the inventors of the air-bailoon. To an elliptical bag of 
silk, 74 feet in length, and 48 in breadth, they attached a 
car for the aerial travellers ; and succeeded in raising this 
immense balloon by itieans of air heated by burning com- 

* For a descriition of balloons, see " Chemistry for Beginners." Page 117'. 

CaiTses nf vnrintions in the temperature of t'le air. Etiect oflieat upon air. 
First atteropi to construct a balloon. Inventor.? of ihe air-balloon. 



SMOKE. 207 

bustlbles in u. grate below the silk bag. A discovery of the 
properties of hydrogen gas, soon caused that substance to 
be substituted for heated air, in inflating balloons. 

Smoke. 

561, The ascent of smoke, is caused by the air being 
made lighter by heat. Smoke consists of the vapour, gases 
and dust, which arise from the fuel, and is borne upwards 
by the rising current of heated air, in the same manner as 
straws and other, light substances are carried along by a 
stream of water. 

562, All that is visible in smoke, is really heavier than 
air, and soon fails, settling upon the sides of chimneys or the 
roofs of houses and surrounding objects, in the form of soot 
or fine powder. As hot air is continually rising in a h6ated 
chimney, its place is supplied by colder air, which in all di- 
rections is moving towards the fire-place to Jill the void. 
This colder air being m turn heated, rises also in the chim- 
ney, which is thus filled with a column of air much lighter 
than a column of atmosphere of the same height, and there- 
fore issues from the top of the chimney, being forced up by 
the colder and denser air which rushes in at the fire- 
place. 

563, You will perceive therefore, that to say the cliimney 
draws smoke, is not strictly accurate, since it is the current 
of heated air which bears the smoke upward. You may 
now understand why a door or window is opened to free an 
apartment from smoke ; a current of freeh air being thus 
thrown in, not only promotes the combustion of fuel, but, by 
its pressure, impels the lighter air of the chimney upwards. 

Why smoke ascends. Wliat smoke consists of. Is smoke lighter than air .'' 
Frocess which goes on in a heated chimney. Chimney does not draw smoke; 



208 NATURAL PHILOSOPHY, 



- LECTURE XXVII. 

WI^'DS THEIR CAUSES AND EFFECTSa 

564. Wind is air in motion. Carrents of air are caused 
by variations of temperature. Wlien any part of the at- 
mosphere is more heated than the surrounding air, it be- 
comes h'ghter, and rises, while the heavier air rushes in to 
supply its place, and this, in turn becoming heated, ascends, 
and thus a current of air is produced, v/hich is always in tJie 
direction ioicards ihe greatest heat. There is a rush of air 
from open doors or windows towards the heated fire-place 
of a room. If, when the air is calm, a fire be made of straw 
or other light combustibles in an open field, currents of wind 
will begin to blow towards the fire. During the conflagra- 
'tion of a building, the same fact will be strikingly manifest- 
ed, for as the heat, and consequently the rarefaction of the 
air is greater, the force of the currents, rushing to take the 
place of the ascending air, is greater. 

565. The sun being the great source of heat to the earth. 
its situation must of course greatly influence the direction of 
winds. If the earth did not revolve on its axis, one portion, 
of its surface being then continually more exposed to the 
rays of the sun, the air would be here most rarefied, and as- 
cend into higher regions, like smoke from a great fire, while 
towards this point would be impelled the surrounding colder 
and heavier air. But as the earth does revolve on its axis, it 
follows, that successive portions of its surface are presented 
to the sun, and become heated ; now as the heated part is 
constantly moving westward, and carrying in that direction 
the rarefied air, there is generally a current blowing in this 
direction, or a constant east wind at the equator. The equa- 
torial region being that part of the earth which is most heat- 
ed, it is here that the equilibrium of the air is most dis- 
turbed, and that winds are most violent and terrific. 

566. The laws of mechanics with resnect to the motion 



Caiise of currents of air. Why does the -wind blow towards a fire ? Cause 
of the constant east winds at tlie equator. Where are tlie winds most violent .' 



WINDS. 209 

which results from the composition of two or more forces, 
influence the action of winds, no Jess than of soKd, moving 
bodies. The direction of the wind may depend on various 
causes, being the resultant of two or more currents, or 
forces. 

567. As we go from the equator to about the 30th degree 
of latitude, the wind is found to vary from the east point, so 
as to become north-east on the northern side, and south-east 
on the southern side of the equator. This is because the 
f^quatorial parts being hotter than any other on the globe, 
the currents of less rarefied air from the north and south 
move that wa}^, but the northern current meeting with the 
eastern, or that which follows the diurnal motion of the earth, 
the resultant is the north-eastern wind ; while the southern 
current also falling in with the eastern, produces, by the 
composition of the two forces, a south-east wind. These 
constant winds which always blow nearly in the same direc- 
tion, from their great importance to navigation and com- 
merce^ are called trcide-winds. They prevail most in the 
Pacific and Atlantic oceans, and in the seas connected with 
them. 

508. There are also in the seas between Asia and the 
equator, the monsoons, or shifting trade-winds ; these differ 
from the constant trade-winds, because they change their 
course every half yea^, when the sun changes its position 
from the northern to the southern side of the equator ; that 
is when from March to September, or when the sun is north 
of the equator, the monsoons blow from the south-west; 
while the remaining part of the year, or when the sun is 
south of the equator, they blow from the north-east. About 
the period of the equinoctial changes, there is a change 
in these winds, or, as the sailors term it, "a breaking 
up of the monsoons ;" the seas where they prevail, are 
then subject to storms, hurricanes and dead calms. The 
Indian ocean is most affected by tliese winds. When 
the sun is north of the equator, the surrounding Asiatic 
coast, being exposed to its direct rays, is hotter than the 
Indian ocean, and the wind blows towards the coast ; when 



Mntion of the wind governed by mechanical laws. Variation of wind as we 
go from the equator. Trade-winds how formed Monsoons. Brealcing up of 
the monsoons. Why the Indian ocean is most ailected by them. 

18* 



210 - NATURAL PHILOSOPHY. 

the sun is south of the equator, the ocean being more heated, 
the wind . blows towards it from the coast. Navigators to 
China and the East Indies, are therefore obhged to pay 
much attention to these winds. 

569. Land and sea breezes are periodical winds which 
change their direction every day; they are chiefly confined 
to tropical regions, where the wind blows towards the coast 
during the day, and towards the sea durnig the night. The 
land reflects the rays of the sun more povvcrfully than the 
water, therefore during the day the air ovei the land is more 
rarefied than that over the water, and rises into higher re- 
gions of the atmosphere, while the surrounding cooler and 
denser air rushes in to fill the void. As soon as the hot sun 
darts his scorching beams upon the islands and coasts of the 
torrid zone, the refreshing sea breeze comes to revive with 
its balm}?- breath the parched land and fainting inhabitants. 

570. Who that contemplates the beautitlil provisions of 
nature can doubt, that nature herself is under the controul 
of a wise and good Director ? How many facts of science 
reveal to us, that the whole creation is but a chain of infi- 
nite and hbrrmonious relations, the one depending upon, and 
influencing the other, and all upheld by one governing and 
changeless mind ! How often in the moral government of 
God, do peace and consolation, like the sea breeze v/hich 
is produced by the scorching rays of the sun, accompany 
the very afflictions that threatened to overcome human na- 
ture ; and how wisely and beautifully balanced, are both 
moral and physical relations. 

571. The land breeze begins at evening to blow towards 
the sea, and continues through the night ; this change 
is owing to the rapid cooling of the air on land, when 
the sun's rays are withdrawn, while the water which 
had absorbed the heat to a considerable depth below its 
surface, has now a warmer and rare ' atmosphere than the 
surrounding coast, and the wind always blows towards that 
point where the air is lightest. This subject may be illus- 
trated by the following simple experiment. In the middle 
of a large vessel of cold water, put a small vessel filled with 
hot water ; the former representing the ocean, the latter, an 
island with the air over it rarefied by heat. Hold a lighted 

Land and sea breezes. Sea breeze. Physical and moral relations. Land 
breeze. Experiment illustrating the phenomena of land and sea breezes. 



WINDS. 



211 




candle over the coid water (at 
A) and blow it out, you will see 
the smoke [v/hich represents the 
denser air] moving towards the 
vessel containing hot water. — 
Now nil ihe larger vessel with warm water, and the smaller 
with cold, and hold the candle over the hot water (at B,) the 
smoke will- move in the direction of the warmer atmosphere, 

Upjjer and lower Currents of Air, 

572. In the torrid zone there is a continual ascent ofrarefied 
air, which spreads to the north at;d south in a direction opposite 
to the trade-winds belo\v„ These upper currents, becoming 
cooled above, at last descend, and mix, with the lower air of 
the northern and southern regions, thus restoring to them 
. Fig. 15S. what they lose by the lower currents 

fijliiL^ijl i, which they are constantly sending to- 



jij wards the equator. In a warm room the 
'" same process of cold air coming in be- 
low, and warm air rushing out above, is 
continually going on. Hold a lighted 
candle at the top of an open door-way, 
and the blaze will be borne outward by 
the current of rarefied air. Place 
another candle at the bottom of the pas- 
sage, and the blaze will Le blown in- 
ward by the counter current of cold air ; 
while half way between the top and bot- 
tom of the passage, the blaze will rise 
or be blown in neither direction. 




perpendicularly, 



Ejfect of Wind upon the Barometer. 

573. Wind may cause the barometer to fall by diminish- 
ing atmospheric pressure, or a quick motion of air in a hori- 
zontal direction, may suspend the whole or part of its weight ; 
as a person in skating rapidly, would pass over ice that 
would not bear his weight if he v/ere standing still. The 
force of a current of air is increased in proportion, as the 



Wliy does not the air of the polar )egions become cxhau?t.cd, by tlie currents 
I o wards the equator ■? Experiment shewing upper and lower currents of" air. 



212 ' NATURAL PHILOSOPHY. 

passage through which it runs is diminished. Take a small 
tube open at both ends, and blow forcibly through it, at the 
same time let alighted candle be placed near to a hole in the 
tube, and you will perceive the flame to be forced towards 
this orifice. While the air with- 

Pjcr, 159, 

''' " ' in the tube was at rest, it exerted 

a pressure against the sides, equal 
to the pressure of air without, 
therefore the two forces balanced 
each other. But when by blow- 
ing through the tube, the horizon- 
tal motion diminished the pressure 
within, the external pressure for- 
ced the air, and with it, the flame 
of the candle into the orifice. You will perceive therefore^ 
that winds, by diminishing atmospheric pressure, must have 
aomiC effect upon the barometer ; and it is found that this 
instrument falls rapidly during high winds. 




LECTURE 'XX. VIII. 

IvIETEOROLOGY. STEAM. ELASTIC FORCE OF STEAM. 
STEAM ExXGINE. 

574. The study of the various changes of weather, with 
the formation of vapour, fog, dew, rain and snow, consti., 
tutes a branch of science called meteorology. Thunder and' 
iightnmg, and all the phenomena of the atmosphere produced 
by electricity, are also the objects of this science, which is 
sufficiently comprehensive to form, of itself, a large volume. 
As a branch of natural philosophy, v/e will make a kw re- 
marks upon some of these subjects, hoping that they may 
lead the investigating pupil to seek in larger works for more 
extensive information. 

575. Evaporation,^ is the slow change of liquids into 

' See Chemistry for Beginners. 2d. Ed. p. 49. 

Atmospheric pressure diminished by wind. What is meteorology 1 



METEOROLOGY. 213 

vapour ; while coiling is a more rapid process of the same 
kind. The sun's rays faUing upon the surface of the land, 
or water, are sufficiently powerful to cause evaporation, or 
to raise into the atmosphere vast quantities of vapour, which 
serves as a storehouse, whence are sent forth, dew, fog, rain 
and snow. Clouds are a collection of condensed vapour, 
which thoLgh invisible near the surface of the earth, where 
the heat is greater, and the vapour consequently rarer, ap- 
pears as a dense mass when cooled in the higher regions of 
the atmosphere. 

576. Fogs are condensed vapour, differing from clouds 
only, in being suspended nearer the surface of the earth. 
When the surface of the earth or water is warmer than the 
surrounding air, the aqueous vapour or watery particles^ 
with v/hich the air in a greater or less degree is always 
charged, becoming heated by a contact with the warmer sur- 
face in attempting to rise, is immediately condensed by the 
colder air around it, and thus a fog is produced. But v/heo 
the air is warmer than the surface of the earth, or the wa- 
ter, the vapour is not condensed, but rises into higher regions, 
forming clouds. 

577. The fogs which often prevail at night, arise in con- 
sequence of the air being cooled more suddenly than the sur- 
face of the earth, by the absence of the sun. When the 
beams of the morning sun begin to warm the earth, we of- 
ten perceive a dense fog arising ; this is owing to the sun's 
rays first heating the earth, because they pass through the 
air without being absorbed by it, air being warmed only by 
contact with a heated body. 

578. We may now understand why in a summer morn- 
ing, fogs are seen hanging over lakes, and rivers ; and why, 
in a cold morning, a vapour like smoke, seems to issue from 
the mouth in breathing : the cause in both cases is the same, 
that is, vapour, in meeting with air colder than itself, is con- 
densed. 

Frost is produced, when the vapour is condensed as soon 
as formed, and is frozen before it can rise from the surface 
of the earth. 

579. Dew is produced when the vapour whicli is formed 
at the surflxce of the warm earth, is condensed before it can 

Evaporation. Fogs. Fogs at night. Fogs at suniise. Viipour which 
seems to issue, frora the mouth i;i breathing. Frost. Dcvv. 



gl4 NATURAL PHILOSOPHY, 

ascend ; and when the surrounding air is not cold enojgh to 
congeal it into frost. Thus it is that the grass and flowers 
are often found covered with moisture, on a summer's morn- 
ing, though there has been neither fog nor rain during the 
night. 

A pitcher filled with cold water, in a warm day, will be 
seen covered with moisture ; this is because the outside of 
the pitcher being colder than the air in contact with it, con- 
denses the vapour which the air held suspended. This 
moisture is formed upon the same principle as dew ; thei cold 
pitcher representing the cold air which condenses vapour 
arising from the earth. 

580. A mist is vapour of clouds becoming more dense, so 
that the aqueous particles acquire sufficient weight to cause 
them to fall, though they are too sm.all to appear visible in 
drops. 

Rain is occasioned by the sudden condensation of aqueous 
vapour, and the consequent union of many minute particles, 
which, becoming more dense, are more readily subject to the 
law of cohesive attraction, and uniting, form drops, which fall 
to the earth by their own gravity. Winds have different ef- 
fects with respect to producing rain. A wind warmer than 
the temperature of the cloud, will dissolve it into an invisible 
vapour, while a colder wind will condense the vapour, and 
cause it to fall in drops. 

.581. Snow is formed by the freezing of minute particles 
of vapour, v/hile they are condensing, and before they have 
formed drops. 

Hail is merely drops of rain, which are frozen in descend- 
ing, by passing through regions colder than those in which 
they were formed. In a warm day we are sometimes sud- 
denly surprised by a hail storm ; this may be occasioned by 
the sudden meeting of hot and moist air, with a very cold 
wind, as the mixture of very hot, and very cold air, is con- 
sidered as one cause of hail. 

582. We find in considering the subject of evaporation 
by heat, tha;t there is a constant change going on, by means 



Dew upon flowers. Cause of moisture on tlie outside of a pitcher containing 
water. Mist. Rain. Effects of wind in producing rain. Snow. Hail. Hail- 
storm in a warm day. Evaporation a source of novelty and beauty in its efftct 

"jpon the aticosph.ci'0. 



METEOROLOGY. "215 

of the ascent of water in the form of vapour, and its descent 
in various forms upon the earth. And how many blessings 
accompany these changes ! To these we owe the variety 
of colouring which we see in the clouds, where, blending 
with the most gorgeous hues, are the faintest and most deli, 
cate tints which nature presents, or imagination can paint. 
The forms of these floating vapours are by turns grotesque, 
picturesque, beautiful and sublime ; — who can tell how much 
of poetical inspiration, of calm delight, and of devout medi- 
tation, the contemplation of them have afforded to the suc- 
cessive generations of men, who, by turns have gazed upon 
their changing forms and colours, as of something belonging 
to another world. How tame and dull would be the aspect 
of the heavens, were they always to present an unvarying 
appearance, even though it were the undimmed calmness of 
a summer sky ! 

583. And again, were the process of evaporation to cease, 
the earth overcharged with moisture, would destroy by this 
excess, the vegetation Vv'hich it now nourishes. There 
would then, no longer be rain or dew, to refresh and purify 
the air. Mountainous regions, after sending forth their v/a- 
tery stores, in rivulets and rivers, would become impover- 
ished and withhold their gifts, while the ocean, losing nothing 
by evapora^on, and swollen by supplies no longer thus ta- 
ken up, would overleap its bounds, and extend its dominions 
over the land. Such must be the consequences of an in- 
terruption in the wise and constant government of God, in 
this department of nature. Yet many of God's creaturesj 
calling themselves rational, never imagine that there is any 
"thing in all this to call forth their gratitude or admiration. 
They are like children enjoying the support and protection 
of a kind and watchful parent, without gratitude, or even a 
consciousness of their obligations. There are men who can 
"bear to live, and dare to die," indifferent to the character 
and requirements of the Being, whose providence not only 
sustains thenij by the general and constant laws with which 
he governs " times and seasons," but who with minute in- 
spection, watches over the smallest circumstance of tlicir 
existence. 



Coadition of l.lie earth s'(.)nl(l tlic process o!" rv;ii)ni-alion cease. 
God's providence mid our ohligations lo grathuic and obedience. 




216 NATUfeAL PHILOSOPHY. 



Steam. 

584. Boiling is a rapid process of converting water into 
vapour, and the vapour thus produced is called steam/^ 
We shall refer you to chemistry for an explanation of the 
process of boiling, and the properties of steam : to natural 
philosophy properly belongs the consideration of its mechani. 
cal agencies. The pressure of the atmosphere opposes it- 
self to the formation of steam, and where this pressure is re- 
moved, liquids can be made to boil with much less heat. 
Even the warmth of the hand is found sufficient to make 
alcohol boil, when relieved from atmospheric pressure. 

The figure lepresents a 
^'°* ■^^°* pulse-glass ; it consists of a 

glass tube v/ith a bulb at each 
end. The glass being partly 
filled with alcohol, and the air 
having been expelled by cau= 
sing the liquid to boil,^the open end is hermeticallyl sealed. 
There is now a vacuum over the liquid ; that is, it is not 
subjected to the pressure of air ;-— on holding in the warm 
hand the bulb which contains the hquid, it will begin to boil, 
and steam or vapour v/ill pass over into the cold bulb, when 
it will be condensed, or again become liquid, until the whole 
contents of the warmer bulb are thus transferred. 

585. Liquids, at the top of mountains, boil with less heat 
than in lower regions, because the pressure of the atmos- 
phere is less. Under the exhausted receiver of an air-pump 
a small increase of temperature will cause a liquid to as= 
sume the state of vapour. 

588. The pressure of the atmosphere prevents steam from, 
rising, on the same principle that any other weight upon an 
elastic body prevents its rising, and the greater this weight, 
the greater must be the power v/hich overcomes it. Heat 
'is the power, which in boiling, causes steam to rise against 

' See Chemi'try for Beginners. 2d. Ed. p. 53. 

t That is, sealed by melting" l!ie glass at one end, and closing it when soft. 

Boiling. Atmospheric pressure opposes the funnation of sleam. Pnlse-glas.'?. 
Liquids boiling at. the fcp of higli mountains. Force which prevents steam 
from 1 i?ing. i-'oi. ti' u'l heat. 



SONOROUS BODIES. 229 

vibratory motion, and give only a confused and imperfect 
sound. 

609. The vibration of a sonorous body gives a tremulous 
motion to the surrounding air, similar to that caused by 
throwing a stone into smooth water. The undulations be- 
come weaker, the farther they are from the centre of mo- 
tion ; it is proved that the intensity of sound decreases in the 
inverse ratio of the square of the distance ; as at 2 rodsdis- 

.tance the sound is 4 times weaker than at one rod distance, 
and at 3 rods distance it is 9 times weaker. 

610. The waves of air producing sound, differ in one re- 
spect from the undulations of water ; air, being elastic, its 
motion does not consist of regularly extending waves, but of 
vibrations, or of motions backwards and forwards, like those 
of the sonorous body. 

Fig. 163. The figure represents these waves 

/^%>. of sound in the atmosphere ; and as they 
^^^ diverge from the point A, it will be 
.-^^ftA^ readily understood that they must become 
■ ^AttBBB weaker, in the same manner that rays of 
"^Tl^^fT light become fainter as they are more dif- 
fused. The points a, h, c, &c., with the intermediate spaces, 
represent undulations of air, spreading in concentric circles 
like waves in a still lake v/hen disturbed. Each particle 
of air, on receiving an impulse, either directly from the so- 
norous body or by transmission, becomes agitated, moves 
back and forth like an oscillating pendulum, within a limited 
space, and at length ceases to move. But it has communi- 
cated motion to contiguous particles, which in their turn, 
vibrate and communicate motion. On account of the ex- 
treme rarity and elasticity of air, vibrations of sound extend 
to a much greater distance than the circular waves of wa- 
ter. The undulations of air being within a sphere, extend- 
ing upwards and downwards as well as outwards, while those 
of water extend only upon a horizontal plane. 

Bells. 
611. It may at first thought, appear incredible that a bell 
actually changes its form every time it is struck ; but it is this 

Cluisg of so'.iiv!. Intensit)' of s'onnd dociviisi^s in thn miio of the distances. 
Waves of ail- dill'T from tlioso of \v;;tir. Dcticiibe ti;e -waves of sound and iti 
transmission throng!) the a'r, 

20 



230 NATURAL PHILOSOPHY. 

circumstance which causes its sound. If hght particles of 
dust lie upon the outside of a bell when it is struck, they 
may be seen to be agitated, which shews that the particles 
of the bell are in motion. A small bit of cork suspended to 
a bell will be tossed back and forth when the bell is sound- 
ing, like a pendulum in motion. 

Fig. 169. 612. Suppose the bell to be struck 

-f on the outside at the point a, this part 

y"a}'\ will tend towards g, while the parts 

/^:^f^^j3!!r^ b and d, tend towards i and m, and 

.-//f 9 \\\"\ this action on these parts causes the 

^fJl j ' j^\ liji^ point c, to approach towards e, but 

"\ u ■ ' / j J owing to the elastic property of the 

\4--'-— ■ ?k/ ' i^etal, these parts soon spring back 

^^^i:^^^::::::::^ to the place where they were when 

'■-P..-'-' the bell was struck, but the momen- 

"' turn they have acquired causes them 

to go beyond this point. Thus the part a, having returned 
from g to a, tends tov/ards/"; the part c towards h ; and the 
parts b and d, towards k and I ; thus though the base of the 
bell is a circle, it is, by being struck, changed into an el- 
lipse, or oval form, of which the diameter is alternately Ion- 
ger in different directions, as is shewn by the figure. These 
ellipses grow smaller and smalleryas the vibrations of a pen- 
dulum Vvhen no longer acted upon by any moving power, 
until the particles ceasing to vibrate, the sound dies away. 
Vv^hen a large bell rings, we perceive a mingling of sounds ; 
this is owing to the difference in diameter of the upper and 
lower parts of the bell. We may consider a bell as com- 
posed of a series of rings placed one above another; those 
nearer the base, having the greater circumference, perform 
their vibrations more slowly than the upper and smaller 
rings, causing, consequently, a variation in the succession of 
sounds. 



idiisical Strings. 

613. The vibrations of musical strings are often visible 
to the eye, and when this is not the case, they may be prov- 



Effect of striking a bell. Describe the figure which illustrates the motion of 
uticles in a sounding bell. Vibrations of iiitisical strings. 



VIBRATIONS OP SOUND. 



231 




^ by experiment. Fine sand or bits of paper will be thrown 
from the strings of a sounding violin or harp. 

It is the elasticity of any 
string which causes a se- 
ries of vibrations, and 
therefore continuance of 
sound. Thus supposing 
a b, to be an elastic string 
fastened at the two ends ; 
on dravv'ing^ this string 
toward c, and then letting it go, it springs back to its straight 
position, but having acquired a momentum like that of a vi- 
brating pendulum, instead of resting here, it passes on tow- 
ards d, nearly as far in the opposite direction. This is one 
vibration ; the momentum then acquired produces other vi- 
brations, each less than the former, until the resistance of 
the air and the friction of the string, overcome the velocity, 
and the string rests in the original position a, h, 

614. Sound is produced by these vibrations in this man- 
ner ; the string strikes against the particles of air v^hich are 
contiguous to it, these particles being condensed by the pres- 
sure, and impelled forward, agitate the surrounding atmos- 
j)here ; each agitation affects the contiguous parts, until th-e 
whole mass within a certain distance assumes a tremulous 
motion. Thus sound does not proceed ft'om a progressive 
motion of air, but from a series of contractions and expan- 
sions of this fluid. 

615. When any sonorous body vibrates, there are cer- 
tain points or lines in its surface, which remain at rest. 
These may be exhibited by experunent; let a pane of window 

i/'i- glass be thinly covered 

with very fine sand, and 
the bow of a violin drasvn 
across its edge ; the mo- 
ment a clear sound is thus 
produced, a part of the 
sand will be thrown olf 
the glass by its vibration, 
while in certain places it remains undisturbed, forming a 



Fit 




Cause of vibrations in strings. How is sound produced by vibrations .'' Rt 
gulur figures produced by a vibrating bod}'. 



232 NATURAL FHILOSOPHV. 

regular figure. The higher the tone, the more complicated 
the figure, thus the figure at A is less complex than at B. 
Another very simple experiment proves also that in vibra- 
ting bodies, there are certain natural stops or rests ; let a 
tumbler be partly filled with water, and draw the wet fxnger 
across its edge until a sound is produced. The vibrations 
of the water will be seen to proceed from certain regular 
points, while there are others in which the water remains 
undisturbed. 

616. A long, vibrating musical string, thus divides itself 
into parts, with points of rest between them, on which points, 
bits of paper will remain, though they will be thrown by the 
vibrating motion from every other part. Thus suppose a h 

Fig. 172. 




to be such a siring, the part from a to d, vibrates as though 
it were fixed at cZ, and so on from d to c, and c to h. " The 
sounds thus belonging to a single cord or string, and pro- 
duced by its spontaneous division into different parts, consti- 
tute when heard together, or in succession, tiie simple music 
of nature herself It is produced in the most perfect man- 
ner by the instrument called the seolian harp. 

617. "The esolian harp is a long box or case of light 
wood, with harp or violin strings extended on its face. 
These are generally tuned in perfect unison with each other, 
or to the same pitch, excepting one serving as a bass, which 
is thicker than the others, and vibrates only half as fast ; 
but when the harp is suspended among trees, or in 
any situation where the fluctuating breeze may reach 
it, each string according to the manner it receives the 
blast, sounds either entire, or breaks into some of the 
simple divisions thus described : the result of which is 
the production of the most pleasing combination and suc- 
cession of sounds that ear has ever listened to, or fan- 
cy perhaps, conceived. After a pause, this fairy harp 

Natural rests in vibrating strings, ^olian harp. 



MEDIUM OF SOUND. 3^33 

may be heard beginning with a low and solemn note, like 
the bass of distant music in the sky ; the sound then swel- 
ling as if approaching, and other tones breaking forth, min- 
gling with the first, and with each other, in the combined 
and varying strain. Sometimes one clear note predomi- 
nates and sometimes another, as if single musicians alter- 
nately led the band : and the concert often seems to ap- 
proach, and again to recede, until with the unequal breeze it 
dies away and all is hushed again. It is no wonder that the 
ancients who understood not the nature of air, nor conse- 
quently of simple sound, should have deemed the music of 
the JEolian harp supernatural, and in their warm imagina- 
tions, should have supposed that it was the strain of invisi- 
ble beings from above, descended in the stillness of evening 
or night to commune with men in a heavenly language of 
^oul, intellio-ible to both."* 



LECTURE XXXI. 



MEDIUx^I OF SOUND. THE EAK. ECHO. SPEAKING TRUMPET. 
VELOCITY OF SOUND. MUSIC. THE HUMAN VOICS. 

Medium of Sound. 

618. Air is the common medium hy loMcli sound is trann' 
mitted ; or in otlier words, the vibrations of sonorous bodies 
cause similar vibrations in the air, which striking upon our 
organ of hearing produces a sensation in the mind. Sensa- 
tion is the parent of perception ; thus the sensation caused 
by vibrations of air produces a perception of sound. 

619. When we hear the sound of a musical string, the 
ear receives from the air as m.any strokes as the string per- 
forms vibrations in the same time. If a string performs 

* Arnott. 

i Medium of sound. Process of the luiad in obtaining a jp(3rcfipi£0» of sound. 
Hjw do vibrations alfcct the car? 

20* 



^34 NATURAL PHILOSOPHY. 

100 vibrations in a second, the ear receives a hundred strokes 
in the same time. 

620. The sound of a bell struck under the receiver^of an 
air.pump, becomes weaker as the air is exhausted, until the 
sound ceases entirely. On admitting air into the receiver, 
the bell will again be heard. When air is more dense than 
common, as in the receiver of a condenser, and in the diving 
bell, sound is more powerful. In accordance with this law, 
it is observed that on high mountains, where the air is light, 
sound is feeble. The travellers among the Alps, say that 
when near enough to see a huntsman on the neighbouring 
chfF and observe the flash of his gun, the report is some- 
times so faint as scarcely to be audible. In caverns and 
mines where the air is usually dense, slight sounds appear 
louder and clearer than at the surface of the earth. 

62i. Liquids convey sounds with... greater velocity than 
air. The sound of a bell, rung under water, and blows of 
workmen in a diving-bell, are heard by people above. Fish- 
es hear the slightest sounds, as the angler may observe^, 
when upon the least agitation of the water above them, 
they are seen to dart off in quest of a more quiet retreat. 

622. Solids convey sounds with greater velocity than air 
or liquids. A long train of iron tubes was laid for the pur- 
pose of conveying water to Paris. M. Biot,* a philosopher 
of great research, took advantage of this circumstance to 
ascertain the exact difference between the powers of air and 
of metal to transmit sounds. He hung a small bell at one 
end of the iron tube in such a situation, that the clapper 
struck against the tube and the side of the bell at the. same 
instant. The sound of the bell was conveyed through the 
column of air enclosed within the tube, while the iron itself 
transmitted the sound made by striking the tube. By the 
person stationed at the other end of the tube, in order to ob- 
serve the succession of the two sounds, it was ascert;iined 
that iron transmits sound with about ten times the velocity 
of air. 

623. If a person at one end of a log, scratt:h the wood 
h'ghtly with a pin, the sound will be heard distinctly by 

' Pronounced Be-o. 

Bell under an exhausted receiver. Sound more powerful as air is more dense. 
Sounds conveyed by liquids. Sounds conveyed by solids. Blot's experiment. 



STETHOSCOPE. 23il 

tinother person whose ear is applied at the other extremityj 
though the air itself would not transmit so feeble a sounds 
By a4)plying the ear to the ground,, the tread of men and 
horses may be discovered, which otherwise could not be 
perceived. Savages avail themselves of this fact to ascer- 
tain the approach of enemies, and animals instinctively re- 
sort to this method for discovering their prey. Previous to 
the great eruption of mount Vesuvius, which buried Ber- 
culaneum and Pompeii, the animals in that region appeared 
disturbed with fears ; this was caused by the agitation of the 
earth produced by distant subterraneous explosions, and 
conveyed by the ground to the ears of these accurate ob- 
servers. 

624. Musical boxes ^ive much louder tones when placed 
upon a table or other solid body, than when air alone is the 
conducting meditim of sound. The vibrations commonicated 
from the box, spreading throughout the particles of wood, 
cause a more extended surface to act upon the air. It is for 
this reason that musical instruments, as violins, guitars, &c., 
are furnished with sounding hoards. If one end of an iron 
poker be placed on the lid of a kettle and the other end held 
to the ear, the boiling of the water will produce a sound 
louder than the rattling of a carriage over a pavement. 

625. The power of solid bodies to conduct sounds, 
has led to the invention of an instrument called the stetho» 
scope* or chest-inspector, the object of which is to convey 
accurately to the ear the sounds produced by the motion of 
the heart, and blood-vessels situated near this organ. It 
consists of a wooden cylinder, one end of which is applied to 
the breast while theear of the physician rests upon the other 
end. " The actions going on in the chest," says Dr. Arnott, 
^' are the entrance and exit of the air in respiration, the voice, 
the motion of the blood in the heart and blood-vessels; and 
so perfectly do these declare themselves to a person listening- 
through the stethoscope, that an ear once familiar with the 
natural and healthy sounds, instantly detects certain devia- 

'^ From the Greek stethos, the bieast or chest, and skopio, to examine. 



Exani|)lrs of tlie power of solids to convej^ sounds. Wliy musical bo.xe& 
should 1)0 placed on a table or solid body. Sounding boards. Kxperiment with 
an iron poker. Stethoscope. 



236 



Natural philosophy. 



lions from them. Plence this instrument becomes a means 
of ascertaining some diseases in the chest almost as effec- 
tually as if there were convenient windows for visual in- 
spection." 

626. " ITe who planted the ear," or tlie organ of hear- 
ing, is also the Creator of the air, or common medium of 
sound, and with that nice adaptation of correspondent means 
to ends, which we behold in all the works of this mighty Ar- 
chitect, we find this organ wonderfully fitted to collect and 
concentrate wa-ves of air, which are caused by vibrations of 
sonorous bodies. The human ear is a curious machine, far 
exceeding in its external construction the most delicate work 
of human art ; and in addition to its various parts, all tending 
to promote the object of hearing, there is an invisible link 
which connects it with the mind, of the nature of which we 
can have no conception. And yet there have been men, 
and those calling themselves philosophers, who, contrary to 
the dictates of common sense and the word of divine revela- 
tion, have asserted that, there is in the universe no great de- 
signer, but, that its creations are the product of mere chance 
or accident. From such philosophers, and from such philo- 
phy, may tlie youth of Anierica be defended ! 

627. We will now examine the parts of the ear, as they 
are manifest by external observation and anatomical dis- 
section. 

1. We perceive on looking 
into the ear, a wide mouthed 
tube, a. This is an ear-trumpet, 
the wide mouth of which serves 
to collect the waves of sound 
which are concentrated at the 
bottom or nervous part of the 
ear4ube. This tube by the ac= 
tion of certain muscles, is movable by many animals, so that 
it can be directed towards the point whence the sound pro- 
ceeds. 

628. 2. The tympanum, or drum of the ear, h, is a tight 
drawn membrane, situated at the bottom of the ear-tube, 
upon which the concentrated sound falls and causes its vi= 



Fig. 173. 




The ear a machine evincing design. 
i)rum of the ear. 



Parts of th€ 



Tube of the ear. 



THE EAR. 237 

bration. The air vntliin the drum commursicates with the 
external air by an open passage f, called the eustachian 
tube, which leads to the back of the mouth. When this tube 
is obstructed by wax, a degree of deafness is produced, and 
the cracking noise' and return of acute hearing, which is of- 
ten caused hy sneezing or coughing, is the effect of the re- 
moval of this obstruction. 

629.: 3c At e is an oval door, or entrance into the laby- 
rinth ; this is connected with the drum of the ear by a chain 
of four small bonesj which serves to convey to the labyrinth 
the vibrations from the drum. 

630. 4. The labyrinth is that complex, inner compart- 
ment of the ear over which the nerve of hearing, or auditory 
nerve, is spread as a lining. Tiiis nerve, like the optic 
nerve of the eye, is a connecting link between the organ of 
sense and the great sensorium, the brain. The labyrinth is 
filled with water, so that when the membrane of the drum, 
acting upon the chain of small bones, compresses the portion 
of waternextthischain, the pressure is instantly felt through- 
out the whole mass of water, and thus the vibration is con- 
veyed to the lining of the labyrinth or the organ of hearing. 

631. The labyrinth consists of the vesiibule or oval door 
e, the three semicircular canals c, which are imbedded in 
the hard bone, and the cochlea, d, which is a winding cavity 
like a snail shell. In this cavity are fibres stretched across 
like harp strings, these are called the lyra, 

632. We judge of the distance of sound by its intensity. 
The ear is capable of determining the direction from which 
sound proceeds. When we are doubtful respecting a sound, 
v/e turn the mouth of the ear-tube towards the point from 
which it seems to issue, and thus learn its nature, distance, 
direction and intensity. 

The phenomena of hearing, considered as a sensation of 
the mind, belongs to the science of mental, rather than me- 
chanical philosophy. 

Reflection of Sound. 

633. An echo is a reflected sound. W^e will explain 
this; the waves of sound or undulations of air moving for- 



Eiilrance into llie labyrl;itli. Tlio labyrintli, Fatts of the labyriutli. Our 
judgment of pounds. Echd, how caused ? 



238 



NATURAL PHILOSOPHY. 



ward, meet with some solid body and are tlirown back, as 
waves of water are repelled by the river bank, or as a mar- 
ble rebounds when ihrown upon the pavement. 

According to a law of motion previously stated,* when an 
elastic body strikes against a hard substance perpendicularly, 
it is reflected back in the same direction, but when it strikes 
obliquely it is thrown off obliquely in the opposite direction; 
that is, the angle of reflection is equal to the angle of in- 
cidence. Now let us apply this to 
sound. Suppose a bell, a, to be struck, 
and the waves of air to full perpendi- 
cularly upon a wall, c, they would be 
reflected back in the line c a ; o, per- 
son situated at any point on ihis line 
would first hear the direct sound of 
the bell by means of the waves of air 
caused by its vibration, and again 
would hear the same when reflected 
from the wall. But suppose the waves of sound strike 
obliquely upon a wall as on the line c 5, the reflected sound, 
like the marble thrown against the floor, would go off in an 
oblique direction upon the other side, and the angle made by 
it, with the perpendicular a b, would be equal to the angle of 
incidence. 

634. Sounds uttered by one standing in front of a build- 
ing, at a certain distance, will be returned in a right lino, 
and the echo will be heard by the person speaking ; but let 
the person stand so that the vibration of sound fall upon the 
wall obliquely, he will not hear the echo, though another 
standing as far on the opposite side would hear it ; — thus 
one person standing at the side of a mirror, sees the image 
of another standing on the opposite side, though he does not 
see his own image. 

635. As a wave of sound rebounds according to the same 
law as a wave of water, or an elastic ball, in order that an 
echo may be perfect, the surface producing it must be 




See paragraph 151, page 59. 



Manner in which sound is refl 'cted. In what case an echo will be heard by 
a persim who utters the sound which is reflected, ^^■hat is necessary in order 
1o .produce a perlect echo 1 



REFLECTION OF SOUND. 



239 



smooth, and of some regular form. The various articles of 
furniture in a room, especially those of a soft texture, as 
carpets and curtains, act unfavourably upon the vibrations 
which produce sounds. The labour of speaking audibly in 
a crowded room is greater than in a room which contains 
few persons. Any one who tries the effect of speaking or 
singing in an empty room, will be sensible that the power of 
sound is much heightened by the vibrations of bare walls, 

636. Plane and smooth surfaces reflect sound without either 
dispersing or collecting it ; convex surfaces disperse, and con- 
cave surfaces collect it. Thus as we shall find in consider- 
ing the subject of optics, plane, convex, and concave mir- 
rors reflect light in the same manner^ for which reason we 
see our own true image in a plane mirror, a magnified and 
distorted one in a concave mirror, and a miniature image in 
a convex mirror. 

•• 637. Suppose e ^ to be a 

smooth concave surface, and 
that waves of sound fall upon 
a, h, c, d, these will be collect- 
ed and brought to a focus* at 
f, and here the echo or reflect- 
ed sound is most perfect. — 
Sound proceeding from the 
centre of a circle is reflected to this point, hence in a large 
circular room we may expect in the centre a powerful echo. 
We say a large room, because sound moves with such velo- 
city that in a small space the reflected sound follows the 
direct sound so rapidly, that they blend together and form 
but one. We shall notice this fact further in treating of 
the velocity of sound. 

638. An oval or ellipse has two centres, or foci,-\ one 
towards each end, as a, and 6; and the nature of the curve 



Fisf 




* A central point. 



t The plural o? focus. 



Speaking in a crowded room. Reflection froni plane, convex and concave 
surfaces. Describe tlie eirect of sound falling upon a smootli concave surface. 



^40 



NATURAL PHILOSOPHY. 




Fio-. 176. is such, that sound, light, or heat, proceeding 
from either of the/be/, as a, is all directed after 
reflection at various points, as c, 6/, e, to the after 
focus, h. A whisper uttered in one focus of an 
/jC'oval room, may therefore be audible to a person 
]-, situated at the other, though it may not be heard 
by persons placed between these two points. The 
celebrated whispering gallery of St. Paul's cathe- 
dral in London, is an example. By a knowledge of this pro- 
perty of sound, the ancient priests were assisted in impos- 
ing upon the people their own words as the oracles of the 
gods. 

639. By the poets of antiquity, ICcho was fabled as a 
wood nymph, who so pined away for love, that nothing re- 
mained of her but her voice. 

The grotto, the cavern, and the mountain side, were con- 
sidered as her peculiar haunts. Every lover of nature is 
pleased in his rambles to find himself accompanied by 
Echo, who, in softer and sweeter tones, reflects his own ac- 
cents. A great musical composer said that Echo was the 
best schoolmistress ; " for, let a man's music be ever so 
good, by playing to an Echo, she would teach him to im- 
prove it." 

640. The speaking trumj)et is constructed on the princi- 
ple that sound may be heightened by reflection. The voice, 

Fig- i^''- insteadof being'dispers- 

ed in the open air, is 
confined within a tube, 
and the vibrjUions fall- 
ing against its sides, are 
reflected and combined 
with those which are moving forwards, and the v/hole thus 
concentrated, moves on to the point towards which tb.e voige 
is directed. The lines within the tube, as seen in the figure, 
represent the manner in which sonorous vibrations are pro- 
pagated through the tube ; F represents the focus or that 




pomt m 



which the waves of sound unite and are most in- 



Sound reflected from an ovt 
FcA'le of echo. Spcaki ng tru mpet. 



WLisj'Ciing g-illery- Ancieut oracles. 



STEAM ENGINE. 217 

'the downward force of the air ; the force of atmospheric 
pressure being equivalent to fifteen pounds on the square 
inch, and 212^ of heat being found sufficient to change water 
into steam, it follows that this quantity of heat can overcome 
a weight of fifteen pounds. In the open air, water cannot 
be made hotter than 212^, since all the additional heat pass- 
es off in the steam. 

587. The peculiar property of steam, and that which ren- 
ders it of such vast importance as a mechanical agent, is its 
great elastic force ; and its property of losing this force by 
being suddenly condensed. " The name of steam engine," 
says Dr. Arnott, "to most persons, brings the idea of a ma- 
chine of the most complex nature, and hence intelligible only 
to those who will devote much time to the study of it ; but 
he who can understand the common pump, may understand 
a steam engine. It is in fact only a pump in which fluid is 
made to impel the piston, instead of being impelled by it, that 
is to say, in which the fluid acts as the power, instead of being 
the resistance. It may be described simply as a strong bar- 
rel, or cylinder, c, with a closely fitting piston in it, at b ; 
the piston is driven up and down by steam admitted alternately 
Fig. 161. above and below, from a suitable boiler ; while the end 

of the piston rod, a, at which the whole force may be 
considered as concentrated, is connected in any conve- 
nient way with the work that is to be performed. The 
power of the engine is of course proportioned to the 
size or area of the piston on which the steam acts, with 
-fa force according to the density, of from 15 to 100 
or more pounds to each square inch. In some of 
the Cornish mines, there are cylinders and pistons 
of more than ninety inches in diameter, on which 

the pressure of the steam equals the effort of six hundred 

horses. 

588. " Sometimes the wonderful piston-rod may be seen 
acting upon one end of a great vibrating beam, with the 
other end of which, immense water-pumps are connected, 
whose motion causes almost a river to gush up from the 
bowels of the earth. At other times workinjj a crank, it is 



Elastic force of steam. Steam engine compared to a punij). How does tlie 
figure illustrate the action of a steam engine 'I To what is the power of the 
Gte'iin engine proportioned ? Various operations of steam engines. 

19 




"218 NATURAL PHILOSOPHY. 

seen urging complicated machinery ; and one engine, 
stretching long arms over a great barrack or manufactory, 
will keep thousands of spinning-wheels in motion, while at 
the same time it is carding the material of the thread, and 
weaving the cloth. In like manner one steam engine in a 
great metropolitan brewery, may be seen at once grinding 
the malt, pulling up supplies of all kinds from wagons around, 
pumping cold water into some of the coppers, sending the 
boiling wort from others up to lofty cooling pans, perhaps 
also working the mash-tub, drawing water from the deep 
wells under ground, loading the drays, and in a word, per- 
forming the offices of a hundred hands. 

" Again there are manufactories where this resistless power 
is seen, with its mechanic claws seizing masses of iron^ 
and in a few minutes delivering them out again, pressed into 
thin sheets, or cut into bars or ribands, as if the iron had be- 
come to it like soft clay in the hands of the potter. One 
steam engine, four miles from London, is at the same instant 
filling all the water reservoirs and baths and fountains of the 
finest quarter of the town. And for some years now, in all 
parts of the world, has this wonderful piston-rod, working at 
its cranks, been turning the paddle wheels of innumerable 
steam-boats, thus setting at defiance the violence of the winds 
and waves, and the currents of the fleetest rivers, while it 
carries men and civilization into the remote recesses of all 
the great continents. Wherever a river leads, the regions 
watered by it, although concealed, perhaps, since the begin- 
ning of the world, are now called by the steam engine from 
their solitudes, to form parts of the great garden, which ci- 
vilized man is beautifying. Such are a few of the prodigies 
which this machine is already performing, and every day is 
witnessing new applications of its utility. 

589. " It regulates with perfect accuracy and uniformity, 
the number of its strokes in a given time, counting or record- 
ing them moreover, to tell how much work it has done, as 
a clock records the beats of its pendulum, it regulates the 
quantity of steam admitted to work ; the briskness of the lire ; 
the supply of water to the boiler ; the supply of coals to the 
fire ; it opens and shuts its valves with absolute precision as 

Application of steam power to inanufoctories. Steam po^ver applied to navi- 
galioii. Meam regulates and records its own motions. 



STEAM ENGINE. 



219 



£0 time and manner ; it oils its joints ; it takes out any air 
which may accidentally enter into parts which should be va- 
cuous ; and when any thing goes wrong which it cannot of 
itself rectify, it warns its attendants by ringing a bell ; yet 
with all these talents and qualities, and even when exerting 
the power of six hundred horses, it is obedient to the hand of 
a child ; its aliment is coal, wood, charcoal or other combus- 
tibles ; it consumes none while idle ; it never tires, and wants 
no sleep ; it is not subject to malady when originally well 
made, and only refuses to work when worn out with age ; it 
is equally active in all climates, and will do work of any kind ; 
it is a water pumper, a miner, a sailor, a cotton spinner, a 
weaver, a blacksmith, a miller, &c. &;c. ; and a small engine 
in the character of a steam poney, may be seen dragging 
after it on a rail road, a hundred ions of merchandise, or a 
regiment of soldiers, with greater speed than that of our 
fleetest coaches. It is the king of machines, and a perma- 
nent realization of the Genii of eastern fable, whose supernat- 
'ural powers were occasionally at the command of man." 

590. No writer has, perhaps, described the parts of a 
steam engine, and their uses, with more clearness than pro- 
fessor Olmstead, in the following extract, from his Compen- 
dium of Natural Philosophy. 

Fior. 1G2. 




" The chief parts of the engine are the boiler A, the cyl- 
inder C, the piston-rod I J, the condenser L, and the uir- 



220 NATURAL PHILOSOPHY. 

pump M. B, is the steam-pipe, branching into two arms^ 
communicating respectively with the top and bottom of the 
cyhnder, and K, is the eduction-pipe,* formed of the two 
branches which proceed from the top and bottom of the cyl- 
inder, and communicate betw^een the cylinder and the conden- 
ser. N, is a cistern or well of coM water in which the con- 
denser is immersed. Each branch of pipe has its own 
valve, as F, G, P, Q, which may be opened or closed as the 
occasion requires. 

591. "Suppose, first, that all the valves are open, while 
steam is issuing freely from the boiler. It is easy to see 
that the steam would circulate freely through all parts of 
the machine, expelling the air, which would escape through 
the valve in the piston of the air-pump, and thus the interior 
spaces would all be filled with steam. This process is call- 
ed blowing through ; it is heard when a steam boat is about 
setting off. Next the valves, F, and Q, are closed, G and 
P, remaining open. The steam now pressing on the cylin- 
der forces it down, and the instant when it begins to descend, 
the stop cock O, is opened, admitting cold water, which 
meets the steam as it rushes from the cylinder and effectu- 
ally condenses it, leaving no force below the piston, to op= 
pose its descent. Lastly, G and P, being closed, F and Q. 
are opened, the steam flows in below the piston, and rushes 
from above it into the condenser, by which means the pis- 
ton is forced up again with the same power as that with 
which it descended. Meanwhile the air-pump is playing, 
and removing the water and air from the condenser, and 
pouring the water into a reservoir, whence it is conveyed to 
the boiler, to renew the same circuit." 

* From educo, to draw out. 

Parts of a steam engine. Action of the steam engine. 



PUMPS, 221 



LECTURE XXIX. 

ATMOSPHERIC PRESSURE UPON WATER. PUMPS. SYPHONSo 

Pumps, 

592. You have seen, in exan:iming the baromet^, that 
i\\(i pressure of the atmosphere is sufficient to support a col- 
umn of 30 inches of mercury, and a column of about 34 feet"*" 
of water. That is, a column of the atmosphere which is sup- 
posed to be nearly 50 miles high, of equal base, is of the 
same weight, and therefore will balance a Qolumn of mercu- 
ry or of water, of the height above stated. 

It is upon this principle that we account for the rise of 
water in a pump, when the air within is removed by pump, 
ing, and the weight of external air meeting with no coun- 
teracting force, -presses the liquid downward. 

There are few children in New England, who have not 
visited the cider-mill in the season for grinding apples, and 
with a straw, drawn the new sweet cider from a barrel. This 
is done by suction ; the air being drawn from the straw by 
the mouth, as it is exhausted from the pump, by the piston, 
in consequence of which, the liquid in both cases rushes up 
to fill the vacuum. 

* Some writers say 32 feet, some 33 feet; — 34 feet is undoubtedly the maxi- 
"Tiwrn height to which a cohimn of water can be raised by atmospheric pressure. 



To what height will the pressure of the atmosphere support mercury or water 
On what principle does water rise in a pump? Suction. 

19* 



222 



NATURAL PHILOSOPHY. 



Fig. 163. 




Suction Pump, 

593. The common household pump, consists 
of a large tube, E, in which is a piston made to 
fit, air-tight, the bore of the tube. In the pis- 
ton is a valve, C, opening upwards like a trap- 
^ door, which allows the air and water to rise 
* through it, but not to descend. This piston, 
sometimes called the bucket, is moved up and 
down by a rod fastened to a handle or lever. 
The pump usually consists of two parts ; the 
upper and wider part, E D, is called the pump- 
barrel ; the piston moves in this ; the part of 
the pump, D B, which is smaller in diameter, is 
called the suction-tube. At the joining of these 
two parts, is a fixed valve, D, which also opens 
upwards. E, is a pipe or spout, serving as a 
passage for the water which is raised. 



594. The parts of the pump being now described, we will 
consider its mode of operation. When the piston is let down as 
low as the fixed valve, D, both valves are closed by their own 
weight. Let the piston now be drawn up as at C, and the col- 
umn of air which rested upon it is also raised, leaving a vacuum 
between C and D ; the air below D being relieved from pres- 
sure, expands, and lifting up the valve, D, passes through it 
and fills the vacuum. A few strokes of the piston thus exi 
hausts the pump of air, and the water, relieved from its 
weight, is forced upward by the pressure of the incumbent 
atmosphere. Rushing up through the suction tube, the wa- 
ter lifts the valve, D, and enters the pump-barrel. When 
the piston now descends, it presses upon the water, which not 
being able to return through tho valve D, pushes up this 
valve C, and when the piston is next raised, all the water 
above it is lifted up, and begins to escape through the spout 
E ; thus when the bucket is raised, the valve I) rises, and 
the valve C falls, and when the bucket is depressed, D falls, 
and C rises. 



Describe the suction-pump. Describe its mode of operation. 



FORCING PUMPo 



223 



595. It should be observed, that although the water is 
raised into the pump-barrel by the pressure of the atmos- 
phere, it is lifted from thence to the level of the spout by 
means of the piston. Therefore as the pressure of the at- 
iTQosphere will sustain a column of water about thirty-four 
feet in height, the valve at the top of the suction-tube may 
be this distance from the surface of the water in^the well ; 
and as the v/ater after passing above the suction -tube, is 
raised by lifting, the height to wliich it is afterwards carri- 
ed, will depend on the length of the piston-rod, and the de- 
gree of strength employed. When we say that water will 
not, rise in a pump above thirty- four feet, we mean only that 
'atmospheric pressure will not raise it above that distance. 



The Forcing Pump. 

596. The forcing-pump consists af a 
barrel, A B, and a piston or forcer C. 
There are two fixed valves, one at D 
and the other at S, in the branching-pipe 
V. The piston is solid, or without any 
valve, therefore the water cannot rise 
above it. When the piston is pressed 
down, the air between that and the valve, 
being subjected to pressure, opens the 
valve S, and passes out at the branching- 
pipe. Thus the valve S answers the 
same purpose as the piston- valve of the 
suction-pump, and the process of raising 
the water until it ascends through the 
valve D, is the same as that which takes 
place in raising it into the barrel of the suction-pump. But 
the water being pressed upon by the piston in the barrel of 
the forcing-pump, and having no other vent, is forced through 
the valve S. 

597. As the operation of a pump consists in applying pow- 
er by separate efforts, it is evident that the water will not 
flow out in a steady current. This effect is produced by 
the addition of an air-vessel, U, into which is fitted a small 




Can water be raised ia a pump higher than thirty-four feel? Describe the 
forcing-pump. How is the water in a forcing-pump made to How out in a steady 
current ? 



224 NATURAL PHILOSOPHY. 

pipe, T, reaching nearly to the bottom of the vessel. This 
vessel by the action of the pump vvill at first be filled with 
condensed air ; when water is forced in through the 
valve S, it v/ill confine the air in the upper part of the ves- 
sel ; on the admission of more water the condensed air pres- 
ses, by its elasticity, on the surface of the water which can- 
not return through tiie valve S, and is forced up the pipe T, 
in a steady stream. Thus the condensed air first receives 
the force given by the piston, and reacts by its elasticity, 
like a spring upon the surface of the water, with a nearly 
uniform power. 

598. The Jire engine consists of tv/o forcing-pumps work- 
ing together ; these throw the water into an air vessel, from 
whence it passes into two long leathern tubes, called the 
hose ; these may be pointed in any direction in order to ex- 
tinguish the fire. 

Syphon. 

599. There is a very simple instrum.ent cal- 
led a syphon, the action of which depends on 
the pressure of the atmosphere. It is used for 
drawing off liquors from one cask into another. 
Suppose a Z* to be a tube having two arms of 
unequal length ; this tube being iilied with wa- 
ter, and the mouth of the shorter arm immer- 
sed in a vessel filled with any liquid, the liquid 
will run out until the vessel containing it is 
emptied. The cause of this action of the sy- 
phon may be thus explained. The liquid which at first fil- 
led the longer arm, would f^ow out by its own gravity, and 
a vacuum being left, the pressure of the atmosphere upon 
the surface of the liquid v/ithin the vessel, would force that 
in the shorter arm of the syphon over the top ; the same cause 
would continue to sustain the shorter column, and to impel 
the liquid over the top until the whole was exhausted. 

600. This effect may be produced with any similar bent 
tube provided the shorter arm or column be less than thirty- 
four feet in length, otherwise the force of atmospheric pres- 



Fire engine. Describe the syphon. Wliy must the short arm of the syphon 
be less than thirty -four feet? 




TANTALUS' CUP. 



225 



rare would be insufficient to force the liquid through the 
Fig. 166. tube. Mercury may be drawn through a 
syphon in the same manner as waterj but 
as this fluid is nearly 14 times heavier, the 
height of the syphon in this case must be 
proportionally shortened, since the mercury 
would only rise about thirty inches, as in the 
barometer. Syphons are sometimes made 
with a suction-pipe, as at a, in which case 

a vacuum may be formed in the shorter arm, by the mouth. 




Fi?. 167. 



Tantalus^ Cup. 



601. An amusing toy called Tan- 
talus' cup,* represents the figure of 
a man standing in a cup. the han- 
dle of the cup is a syphon ; the short 
arm of which is nearly level with the 
mouth of the figure, pouring water 
into the cup it continues to fill, until 
the liquid is near the mouth of the 
figure, and if raised higher, it flows 
out through the syphon handle. 



602. Intermitting springs or fountains, are caused by 
drains in the earth communicating with reservoirs of water. 
These drains may be considered as natural syphons, which, 
acted upon by atmospheric pressure, carry off the water, 

For the gratification of pupils who may not be famihar with the fable of 
Tantahis, we Avill inform them that in mytliology, he is represented as having, 
for an offence against Jupiter, been phmged from a state of happiness into one of 
torments. His greatest punishment was that of everlasting thirst; being con- 
demned to see a pure stream forever rising to his lips, but ilowing back as soon 
as he attempted to drink of it. This fable is considered as emblematical of unsat- 
isfied desires. 




Why must a syphon for drawing mercury be shorter than for water.'' Sy- 
phon with a suction-pipe. On v/hat principle is the toy called Tantalus' cup cob- 
^ructed i* Intermitting springs. 



226 NATURAL PHILOSOPHY. 

and then cease flowing until rains or the mehing of sno'.vs, 
have again filled the reservoirs. 

603. We shall now conclude our enquiries into the sci- 
ence of pneumatics, after enumerating some of its leading 
principles. 

1. Pneumatics treats of the mechanical properties of elastic 
fluids, chiefly of air. 

2. Air is MATTEK, as it is extended and imjjenefrahle. 

3. Air is invisible, because it is thin and transparent. 

4. Air possesses weight ; it is compressible and elastic. 

5. The elasticity of air, or its sp-ing, increases with its 
density. 

6. The density of the air diminishes upwards, or its pres- 
sure is in proporlion to its depth. 

7. The air like water presses in all directions. 

8. The pressure of the atmosphere on fMids causes the rise 
of water in pumps, and of mercury in the barometer. 

9. The air-pump is an instrument used for exhausting the 
air from any vessel. 

10. A vacuum is an empty space, or generally understood 
to mean a. space emptied of air. 

11. A condenser is an instrument used for the purpose of 
pressing more air into a vessel ; the air is said to be con- 
densed, because it is heavier than common air. The ope- 
rations of the air-pump and condenser are directly opposite, 
'because the former rarefies, and the latter condenses air. 

12. The barometer measures the weight of the atmos- 
phere, the thermometer its temperature. 

Leadiag- principles in pneumatics. 



PART V 



ACOUSTICS. 



LECTURE XXX. 

SONOROUS BODIES. BELLS. MUSICAL STRINGS. AEOLIAN 
HARP. 

604. Acoustics is a word derived from the Greek, and 
signifies the science which treats of sounds. This subject 
opens to us a train of moral reflections, as well as a curious 
and interesting field of scientific enquiry. The tender ac- 
cents of affection, the solemn tones of prayer, the thrilling 
notes of music, the pealing of bells, and the burst of thunderj 
all, are but vibrations of air. Deprived of sound, what a 
gloomy vacancy would exist in creation, and be felt in the 
heart of man. How grateful to our hearts is the music of 
nature, as heard in the lively carol of birds, the lowing of 
kine, with all the variety of sounds by which the brute crea- 
tion, in their own true and expressive language, manifest 
their emotions. Inanimate nature, too, seems by this won- 
derful gift of sound, to be endued with life and intelligence; 
the brook softly murmurs in its placid course,— the cataract 
in startling thunderings proclaims its tremendous force ; — ■ 
the light foliage responds to the gentle music of the sum- 
mers' breeze; and bending forests, in mournful and myste- 
rious tones, waft to our spirits, upon the wings of the autum- 
nal blasts, thoughts of the majesty and power of Him, " who 
walketh on the wings of the wind." 

Definition of acoustics. Moral reflections upon sound. 



228 NATURAL PHILOSOPHY. 

605. But interesting as is the voice of animate and inani- 
mate nature, we value sound chiefly for the j^oiuer it gives 
us of communicating with mind. 

As sensation is to the soul the medium of holding com- 
munion with external objects, so is sound among human be- 
ings, and even among the brutes, the link which connects 
their sympathies, the chain which binds their affections. 
To this power we are indebted not only for spoken language, 
but for its subsequent expression in written characters, and 
consequently for all human sciences, and divine revelation. 

606. But we will now turn our attention to the philoso= 
phy of sound. 

"The air is vehicle of sound; 
Remove but the elastic pulse of air 
And the same ear wliich now, delighted, feels 
The nice distinction of the finest notes, 
Would not discern the thunder from a breeze." 

607. 1. Bodies which produce sound are called sonorous 



2. Air is the common medium ichich transmits souiid ; 

3. The ear is the organ which receives the impression. 

4. The mind only is capah-e of the sensation produced hy 
sound ; 

5. This sensation is called hearing. 

Sonorous Bodies. 

608. Bodies are properly called sonorous, which afford a 
sound distinct, and of some duration ; such as bells, and the 
strings of musical instruments. Bodies which only cause a 
confused noise, like that of a stone falling upon a pavement, 
are not called sonorous. Thus philosophers make a dis- 
tinction between sound and noise. 

Sound is supposed to be produced by motion in the air 
caused by vibrations of the sounding body. Gold, brass, cop- 
per, silver, iron, and glass, being dense and elastic, are sono- 
rous ; while lead and wax being softer, are less capable of 



Chief value of sound. What philosophical truth is expressed in the quotation 1 
Repeat the five propositions respecting sound. Sonoi'uus bodies. Difference 
between sound and noise. 



EAR TRUMPET. 241 

tense.* The speaking trumpet is of great use at sea, en- 
abling the commander of a vessel to make his voice heard 
amidst the " sound of waters," and in the most violent tem- 
pests. 

641. The ear trumpet is wider where the sound enters, 
and narrower where it is applied to the ear ; its sides are so 
curved, that according to the law of reflection, all the sound 
which enters, is brought to a focus in the narrow end. The 
intensity of sound is thus greatly increased before it reaches 
the ear, and the deaf, by means of this invention, are ena- 
bled to enjoy the conversation of friends, f 

Some sea shells, from their concave, polished surfaces, are 
remarkably adapted to collect and concentrate the waves 
of sound ; when properly fitted with a small tube, a shell 
of this kind forms an elegant and useful ear trumpet. The 
resonance of sound within a large sea shell, is often a cause 
of wonder to the 3^oung, who are almost ready to fancy they 
hear within it, the roaring of that distant ocean of which it 
was once an inhabitant. 

Velocity of Sound. 

642. Sound, though it moves with great velocity, is less 
rapid in its progress than light. The lightning is seen be- 
fore the thunder is heard, though the same electrical dis- 
charge is the cause of both. The flash of a gun, at a 
little distance, is seen before the report is heard. The axe 
of the distant labourer may be seen to fall before the sound 

* Some writers object to the theory of sound being multiplied b}'- reflection 
from the sides of the trumpet, but consider the sound of this instrument "as 
merely the longitudinal vibration of a body of air, to which momentum is given 
in the direction of the axis, not hj reflection from the sides, but by the direct im- 
pulse of th'^m both." 

t It is of late found that tubes ofindian rubber answer even a better purpose 
than tbe common ear trumpet. From the nature of this substance, tubes may be 
made of a much greater length thnii could be conveniently used, if formed of an 
inflexible material ; ancJ it. is ascertained, that the longer the conducting tube, the 
more intense is the sound. Thus, M. Biot, of Paris, found that aqueduct tubes 
a mile in lengtli, conducted sounds, the most feeble and as he expressed it, the 
only way to prevent being heard at the opposite exti cmity of the tube " was not to , 
speak at all." 

Ear trumpet. Shell ear trumpet. Sound moves with less velocity thaur 
light. 

21 



242 NATURAL PHILOSOPHY. 

of the blow is heard; this does not reach the ear until th6 
instrument is rising for another stroke. 

643. It is ascertained that sound moves through the at- 
mosphere at the rate of 1142 feet (nearly a quarter of a 
mile) in a second. We may determine the distance of a 
thunder-cloud by noticing the number of seconds which 
elapse between the lightning and the thunder. Since the 
pulse of a healthy person beats, about once in a second, each 
pulse will indicate a distance of about a quarter of a mile. 
Thus, sixteen beats between the lightning and the report, 
would indicate a distance of about four miles, thirty-two 
beats, eight miles, &c. 

The distance of a ship at sea may be determined, by ob- 
serving the time which passes between the flash of a gun 
fired from it, and the report of the same. 

644. The quickness with which an echo is returned, may 
also serve for a measur? of distance. Thus, suppose a 
cliff upon the opposite bank of a river to return an echo in 
one second ; as sound travels 1142 feet in a second, the 
breadth of the river must be half this distance, or 576 feet ; 
since one second elapses while the sound is going and re- 
turning. 

Ulusic. 

645. The natural music of birds, and the power of singing 
or producing agreeable notes by the human voice, led, in the 
course of ages, to the contrivance of stringed instruments, 
as the harp, lyre, &c. ; and to the invention of wind instru- 
ments, as the pipe, &c. 

646. In stringed instruments, the air is struck by the 
string, and the vibrations of the air produce a corresponding^ 
sound in the ear ; but in pipes, the air is forced against the 
sides of the tubes by the breath, and its vibrations or tones 
areproduced by the reaction of the sides upon the air. 

Sound is varied by the rapidity and momentum of the vi- 
brating body ; and this depends on the length, tension, and 
size of^ the string. A short string vibrates more quickly 

Distance of a thunder cloud ascertained by observing the time between the 
lightning and thunder. Ship at sea. Echo, a measure of distance. InvenUon 
of musical instrumenfs. Diilerence in stringed instruments and pipes. Cause 
~of the variety of sounds. 



MUSIC. 243 

than a long one, and therefore produces the sharpest and 
and highest tones ; and a short and small pipe, from a like 
cause, produces sharp tones ; and large pipes, grave and 
deep sounds. 

647. Savages discovered this ; and they made, and still 
make,simple instruments, which please themselves and their 
wild companions. But art and science go further ; they 
ascertain the causes of the pleasure derived from musical 
sounds, and thus proceed to complex inventions in order to 
afford a higher gratification. 

Hence it was long since found, that if two strings of a 
harp were of equal lengths, they produced the same tone, or 
vibrated in unison. They produce the same number of vi- 
brations, exactly in the same time; their vibrations, if struck 
together, accord; hence they produce the same sound to 
the ear. 

64S. It was afterwards found, that if one of these strings 
were equally divided, the vibrations became half the length 
of the vibrations of the whole, and the note twice as acute ; 
but as every other vibration of the half string corresponds 
with every vibration of the whole one, there is a constant 
unison or concordance between them ; they harmonize or 
vibrate together, for once in the long string, or twice in the 
short one. Hence, there is no jarring or discord ; but they 
are said to be in concord ; and in regard to intervening 
subdivisions, have been made octaves. 

649. But as a harp, composed of strings of only two 
lengths, would produce little variety of sound, it was justly 
considered that if other strings could be contrived, whose 
vibrations corresponded even with less frequency than the 
octave, the compass and variety would be increased without 
d scord. 

Hence, as the number of vibrations of a string is 1, 
whiie that of its octave is 2 ; the next division would be, 
to produce a string which, while the original vibrated 
2, the next should vibrate 3 ; this was done — and this 
note, which is two thirds of the original, is called a fifth. 
A harp, constructed of strings divided in this manner, pro- 
duces an agreeable melody ; the vibrations according and 

Simple instruments. Accordant sounds. Octaves. Fifths. 



244 NATURxVL PHILOSOPHY. 

agreeing with one another at equal intervals, although the 
tones are different. 

650. The strings of a piano-forte, harp, or violin, are- 
brought into accordance or successive octaves, or recurring 
tones, by the accuracy of the ear. 

In the harp, and other instruments, the length of the 
strings is exactly proportioned to the scale, by the maker ; 
but as the strings vary in their tension^ owing to the 
weather, and other causes, and as they cannot all have 
precisely the same bulk, it is necessary, from time to time, tc 
tone them ; which means nothing more than making each 
perform its proper number of vibrations in relation to the 
other strings. 

651. When an agreeable succession of simple notes, hav- 
ing a perfect beginning and ending, is played or sung, it is 
called an air, or melody ; as a song, hymn, or march, ac- 
cording to its several purposes. When these notes, forming 
an air, are combined with corresponding notes, in different 
octaves or on other instruments, and the whole is scientifi- 
cally made to produce a concordant and agreeable effect, 
it is called Harmony. The bass and treble of a piano-forte 
played at the same time with the letl and right hand, con- 
stitute the most common instance of harmony. Some of 
Handel's pieces have been played by 1000 instruments and 
voices, all sounding harmoniously together. 

The Human Voice. 

652. Ancient physiologists considered the windpipe* as 
the immediate organ of sound, and that the voice was caus. 
ed by the action of air against its sides, as sound is produced 
in musical pipes. But the ancients erroneously imagined 
this action of the air to be produced as it was passing into 
the lungs, or in the inspiration of the breath ; whereas, it is 
now understood that the voice is formed during the expiration 
of air, or in its passage from the lungs. The lungs may 
be considered as performing the same office in propelling air 
into the windpipe, as the bellows of an organ in blowing air 
into the pipes of that instrument. 

' Technically called the trachea. 

To.iing musicalinstruments. 'R&xmonj. Formation of sound. 



THE HUMAN VOICE. 245 

firs. The parts which are essential to the production of 
vocal sounds, are the lungs, ivindpipe, larynx, and glottis. 
Respecting the action of the lungs, and the effect of air upon 
them, we have previously made some remarks.* The wind 
or air pipe, is a cartilaginous tube, through which the air 
passes to and from the lungs ; the larynx is an enlargement 
of the windpipe, situated at the back of the mouth. Just be- 
low the larynx, is the glottis, a smaller passage, furnished 
with muscles, for contracting, enlarging or altering its form 
so as to produce a great variety of sounds. Indeed it is 
principally to the powers of this small organ, that we attri- 
bute the phenomena of vocal sounds, 

054. If the wind pipe below the glottis is perforated, so 
that the air in expiration issues at the orifice, there is no vo- 
cal power ; but it is otherwise with an injury to the throat 
which does not affect the glottis. Naturalists say that even 
the windpipe and larynx may be taken from an animal, 
without destroying its voice. Baron Cuvier asserts that 
having cut off the head of a bird, without injuring the glottis, 
the headless animal uttered several cries. Some curious 
naturalists who have experimented with the vocal organs of 
a pig, by fitting to the windpipe the bellows of an organ, 
which answered the purpose of the lungs, and varying the 
aperture of the glottis by pressure with the fingers, have 
succeeded in imitating with this apparatus, the grunting 
sound peculiar to the swinish race. 

655. By observing the formation of the vocal organs in 
man, mechanicians have succeeded in constructing instru- 
ments which articulate letters, and even words and senten- 
ces. A German,, who made himself famous for the inven- 
tion of an automaton chess-player, is said to have succeeded 
in constructing a speaking machine which can talk in French 
and Latin. ^ It is gravely suggested by some men of science, 
that from the discoveries made of the mechanism of the vo- 
cal organs, and the nature of the human voice, it may be 
possible to construct machines for the pronunciation of mod- 
ern languages, so that our language may be transmitted to 

* See Pneumatics, H 577. 

Organs ofsouiid. Experiments wiih the vocal organs of animals. Speaking 
macliines. 

21* 



2AQ NATURAL PHILOSOPHY. 

the ear as well as to the eye of future generations. A ma- 
chine which could talk like an ancient Greek or Roman, 
would be a truly valuable addition to a school or college 
apparatus, but it is somewhat doubtful whether its discourse 
would be understood by many learned teachers, who now 
imagine that they have the true pronunciation of Demosthe- 
nes and Cicero. 

656. But with all man's invention, we cannot seriously be- 
lieve him capable of succeeding in any attempt to make aZiv- 
ing, hreathing, thinking, or talking machine. In fact, the 
greatest efforts of human ingenuity, when compared with the 
productions of nature^ are as the rude attempts of an unskilful 
hand in touching a musical instrument, to the perfection of a 
finished performer, who knows the exact powers of every 
key, and how to mingle sounds to produce a varied and me- 
lodious harmony. The imbecility of man must ever appear 
when he directs his efforts into the region where God works ; 
when he attempts to produce phenomena analogous to those 
of life. Man may copy, hut God only can create. 

Limited power of man. 



PART VI 
OPTICS. 



LECTURE XXXIL 

LIGHT. DEFINITIONS. MOTION OF LIGHT. ITS INTENSITY. 
OF REFLECTION, REFRACTION AND INFLECTION. 

Preliminary Remarks on Light. 

657. By means of the sense of seeing, we become ac- 
quainted with the powers and properties of light. The sci- 
ence which treats of Hght and its effects is called optics. 
This term is from the Greek, and signifies " relating to 
sight ;"— the word optic, signifies an organ of sight or vision, 

658. So important is vision to man, that, as we should 
naturally expect, light and its phenomena earl}^ received the 
attention of philosophers. The science of optics is among 
the oldest branches of natural philosophy. Some of its 
most important principles were suggested by Plato and Aris- 
totle. To the moderns, however, we are indebted for the 
invention of many of the most valuable optical instruments. 

659. Philosophers have investigated the nature and ef- 
fects of light, and poets have sung of its glories, but the en- 
lightened christian, to philosophy and poetry, adds the horn, 
age of a devout and pious heart. He considers whose spirit 
it was that moved upon the dark and formless void ; — who 
it was that said " let there be light," and who, in view of the 
comfort and enjoyment this light would bestow on his crca- 
tion, pronounced it " good." 

Definition of optics. Antiquity of the science of optics. Tlie christian's view 
ofliffht. 



248 NATURAL PHILOSOPHY. 

660. The nature of light is not known. It is generally 
believed to be matter, since in its motions it obeys the laws 
which govern matter. It is closely connected with heat and 
electricity, and there are some reasons for the belief that 
they are all but different modifications of the same sub- 
stance. 

661. Sir Isaac Newton supposed rays of light to consist 
of minute particles of matter, which are constantly emana- 
ting from luminous bodies, and cause vision, as odoriferous 
particles, proceeding from certain bodies, cause smelling. 
This is called the system o^ emanation. Some philosophers 
affirm that light is nothing more than the agitation of a me- 
dium called ether, which is far lighter and more subtle than 
air. They suppose that rays of light are produced by vi- 
brations or undulations of tliis ether, as sound is produced by 
vibrations of air. One of the most celebrated advocates of 
the theory oi undulations and vibrations, is Euler, who flour- 
ished in Germany, in the eighteenth century. But the be- 
•ginner in science would profit little by attempting to enter a 
field of controversy in which the greatest philosophers have 
found themselves wandering blindfold among luminous and 
opaque bodies, searching for light, but finding none. It is 
here as in other departments of science, if we limit our enqui- 
ries to the powers and qualities of bodies, we find our toil 
amply rewarded ; but if we attempt to lift the veil which God 
has interposed between us and the secret elements of which 
he formied matter, we find our grasp eluded, and our search 
confounded. 

662. It is not then the nature, absolutely, of light which 
is to engage our enquiries, but the effects of light upon other 
bodies, and how light is affected hy them. To assist us in 
determining how light affects other bodies, let us for one 
moment close our eyes, — the instant void which succeeds 
will serve to shew us, what would be the consequences of the 
absence of light ; — we open our eyes and ten thousand ob- 
jects are before us. The glories of the heavenly arch — the 
beauty, the sublimity of nature in its endless variety of form 
and colour, would but for light, exist for us in vain. 



Nature of light. Newton's bj'pothesis respecting the nature of light. Hypo- 
thesis of Euler and others. What are to be our enquiries respecting light? How 
li^ht aflfects other bodies. 



DEFINTIONS. 249. 

The manner in Vv-hich light is affected hy oilier bodies, in- 
volves some of the most important principles in optics, as 
rejection and refraction. 

Definitions. 

663. Lurainous todies are of two kinds ; those which 
shine by their own light, as the sun, a lamp, or fire, and 
those which shine by reflected light, as the moon. 

Transparent or diaphanous^ bodies are such as permit 
rays of light to pass through them. A perfectly transparent 
body is invisible, as air, when free from vapour of all kinds. 
Water is not perfectly transparent, since it is visible, which 
is also the case with the clearest glass or gem. 

Translucent bodies permit light to pass faintl}^, but with- 
out representing the figure of objects seen through them, as 
china ware, and alabaster. 

Opaque bodies permit no light to pass through them, as 
wood, stone, &;c. Such bodies reflect light, and by this 
means, not only render themselves visible, but diffuse light ■ 
around them, as the moon and stars. 

A ray is a line of light. 

A learn is a collection of parallel rays. 

A pencil is a collection of converging, or diverging rays. 

A medium is any space through which light passes. A 
perfect vacuum is a. free medium. Air and glass are trans- 
parent mediums. I 

Parallel rays are such as proceed equally distant from 
each other through their whole course. 

Converging rays are such, as proceeding from any body, 
approach and tend to unite in a point ; this form of rays is a 
cone. 

Diverging rays are those which proceeding from a point, 

Diaphanous is from the Greek diaphanes, signifying shining through, 
and is S3monymons with tiansparent. 

t The plural of medium, according to Latin analogies, is media, but, as it is 
not inconsistent with good usage, we shall give it the English foim of the plural 
number. 



How affected by them. Luminous bodies. Transparent bodies. Translu- 
cent bodies. Opaque bodies. A ray. A beam, A jiencil. A medium. Pa- 
rallel rays. Converging rays. Diverging rays. 



250 NATURAL PHILOSOPHY. 

continue to recede from each other ; this form of rays is an 
inverted cone. 

K focus is that point at which converging rays meet. 

Motion of Light. 

664. 1. Light moves in straigJii lines. Rays of light 
are projected from a luminous body in every direction, but 
always in right or straight hues ; these lines cross each other 
at every point, but the particles of which each ray consists, 
are so minute, that the rays do not appear to be in the least 
impeded by each other. Wherever a spectator is placed 
with respect to a luminous body, every point of that part of 
the surface which is turned towards him is visible ; this 
shows that the light is emitted in all directions. 

A ray of light passing through an aperture into a dark 
room proceeds in a straight line. 

V/e can see objects through a straight tube, though not 
through a curved one, but we can hear through a bent tube ; 
this proves that the radiation of light is not governed by the 
same law^s as that of sound. Because light moves in straight 
lines, if a number of objects of the same height, be placed in 
a row from the eye, the nearest one hides the others ; as for 
example, a row of trees, or a line of soldiers. 

665. 2. Light movzs wilh great velodty. When a gun is 
fired, we see the flash before we hear the report, and light- 
ring precedes the thunder ; these facts prove that light moves 
with greater velocity than sound. 

666. Astronomy has enabled men not only to foretell 
eclipses of the heavenly bodies, but by means of these eclip- 
ses to ascertain the rate at which light travels. 

The planet Jupiter has four moons, which revolve about 
him as our moon revolves about the earth ; they are subject 
to frequent eclipses, and from the same cause as that which 
produces eclipses of our moon, viz , the entering of the sat. 
ellite into the shadow made by the primary, or, in other 
words, by the primary planet interposing between the satel- 
lite and the sun. By means of the telescope, a satellite 

Focus. jVIanner in wliicli light is radiated. Radiation of light not governed 
bv tlie same laws as that c f sound. Velocity of light compared with that of 
Bound. Velocity of light calculated by means of the eclipses of Jupiter's sat- 
ellites. 



INTENSITY OP LIGHT, 



251 



Pier. 17S. 



of Jupiter may be seen eclipsed ; — the time of its entering 
.and emerging from the shadow cast by the planet, may be 
exactly known by the changes which it presents. Astrono- 
mers calculate the exact moment of these changes as viewed 
from the sun, S. But sometimes the 
earth and Jupiter are on the same side 
of the sun, and sometimes on opposite 
sides ; in the latter case the earth is 
farther from Jupiter, by the whole di- 
ameter of its orbit, or 190,000,000 of 
miles, than when the two planets are 
on the the same side of the sun. It is 
found by observation, that when the 
earth is nearest to Jupiter, an eclipse 
of one of his satellites is seen some 
minutes sooner, than when the earth is 
at its greatest distance from that plan- 
et. This proves that light moves. 
Let S represent the sun, A and B the 
earth in different parts of her orbit, d, 
Jupiter, D, his nearest sateUite, entering the shadow of that 
planet, and C the same sateHite emerging from the shadow. 
When the earth is at A, the eclipse takes place about 8 
"minutes earlier than the calculated period, and when at the 
part of her orbit B, or most distant from the planet Jupiter, 
about 8 minutes later ; that is, about 16 minutes of time 
'elapse while light is travelling across the earth's orbit, 190- 
•000,000 of miles, or from A to B. By an arithmetical cal- 
culation we find, if light travels a distance of one hundred 
and ninety millions of miles in 16 minutes, it moves at the 
rate of about 197,916 miles in one second.* 




Intensity of Light. 

^ 667. The light diffused by a luminous body becomes 
fainter with increasing distance. Thus suppose « to be a 

* 190,000,000 -^ 16 X 60 = 197,916. 



Dimiuislied intensity of light. 



"252 



NATURAL PHILOSOPHY. 




179. luminous body radiating light in all di- 
rections; now as the same proportion of 

light illumines the space within the circle 

^ ^a ^ ^^ as within the circle e d, it is evident 
^B that c b must be the more strongly illumi- 
^ nated. At d, which is twice the distance 
m^^m^ of b from the candle, the intensity of hght 
is four times less than at b, at three times 
the distance it would be nine times less, at four times the dis- 
tance it would be sixteen times less, and so on; for diver- 
ging rays of light diminish in intensity as the squares of the 
distance increase. 

668. Suppose before the candle a, are placed three square 
boards, h containing 1 square inch, c 4 square inches, and d, 
16 square incheSo Let b be placed at the distance of 1 foot 

Fig. ISO. 






from the candle, c 2 feet, and d 4 feet. Here the smallest 
board b, will obstruct all the rays of light which would other- 
wise fall on c ;. and if ^ were removed, c would in hke man- 
ner hide the light from d; now if the first board receive as 
much light as would fall on the second, whose surface is 
four times as large, the light must be four times as power- 
fid, and sixteen times as powerful as that vdiich vrould fall 
on the last board, because the same quantity of light is dif- 
fused over a space sixteen times greater. The light of a 
candle can be p-erceived, in a clear night, at the distance of 
one or two miles, if not obstructed by intervening objects. 
As sound within a certain distance dies away, and is lost in 
silence, so light \nsQns\h\y fades into darkness. 

Of Refection, Refraction, and Inflection, 

669. The term reflection, as used in optics, signifies the 
rebounding of light from surfaces on which it falls. Here 



Rule for calculatinsr the diminution of light. Reflection. 



INFLECTION. 253 

Vve see light following exactly the same law as is common 
to all matter, thus affording a proof that it is itself a material 
agent. But all bodies do not reflect light.; it is only polish- 
ed surfaces which have this property ; and of such surfa- 
ces, some, as diamonds and glass, may transmit, without re- 
flecting light. Mirrors derive from reflection their pro- 
perty of throwing back the image of an object. 

QlO.'Refr action, "^.diQnoies, the bending of the rays of light, 
as they pass from the surface of one transparent medium to 
another. Thus in passing from air into glass, all the rays, 
except those that fall perpendicularly, are turned from their 
straight course, or, as is expressed in optics, they are refract- 
ed. To the refraction of light v/e are indebted for the pow- 
er of the lenses, or magnifying glasses, which are used in 
the manufacture of spectacles, telescopes, and microscopes. 
It is indeed to the refraction of light, as it passes through the 
different lenses of the eye, that this organ owes its power of 
seeing. "j" 

671. Ir)jiection,X signifies the turning of rays of light from 
'their course, by the attraction of opaque bodies. If a beam 
of light be admitted through a small aperture into a dark 
room, and the edge of a knife or any other thin metallic 
plate be brought near the bean>, the rays of light which 
would othervv'ise have proceeded in a straight line, will be 
inflected, or turned towards the knife. On placing the edge 
of another knife very near to that of the former, the stream 
of light divides in the middle, and leaves a black stripe, indi- 
eating that all the light has been attracted from that space, 
towards ihe two edges. As the knives are brought nearer 
to each other, the dark stripe widens, till, upon the contact 
of the knives, the whole light vanishes. Fringes of different 
coloured light appear on the edges of the two knives, three 
separate fringes on each, and all varying in their colours ; 
the first fringe beginning with violet and terminating with 

* Refraction is so ciillod from tlie Latin prefix, re, ZLndfraJigo, to brealf, on 
account of tlie broken appearance of a ray of light. 

t Tiiougli in accordance with the common use of language, we sa}', the eye 
sets, it should be understood that the seeing is, in reality, in the mind, to which 
the eyes are but the spectacles. 

t From the Lalin verb ivfl.ecto, to ci ook, or bend in. 

Surfaces wlii^cli reflect light. Refraction. Inflection, 

22 



254 NATURAL PHILOSOPHY. 

red, the second beginning with deep blue and terminating 
with red, the third beginning with pale blue and terminating 
with pale red. As the separation of light in the rain-bow, 
is the effect of refraction, we may conclude that by inflec- 
tion, the different coloured rays being differently acted 
upon, a similar decomposition of light is produced. When 
we look at a candle with the eyes almost closed, fringes of 
light appear ; the eyelids v/ill in this case, cause the inflec- 
tion of the beams of light which enter them. 

Thus we find that light may suffer a change of direction 
without actually infringing on a body, but merely by coming 
within the sphere of its influence ; as one body gravitates 
towards another, as the needle is attracted by the magnet, 
and as one body in a different electrical state from another, 
is drawn towards it. 

The inflection of light is rather to be regarded as a curi- 
ous optical phenomenon, than studied in relation to its bear- 
ing upon any known laws, or important apphcations of sci- 
ence ; but refliection wadi refraction are subjects which must 
be attentively studied as the two fundamental principles of 
optics. 



LECTURE XXXIII. 

3EFLECTI0N FROM MIRRORS. PLANE MIRRORS. CONVES: 
MIRRORS. CONCAVE MIRRORS. 

Angles of Incidence and Reflection. 

672. A ray of light turned back into the same medium in 
which it moved before its return, is said to be reflected. 

Incident^ rays, are those which fall on the surface of a 
body ; reflected rays, are those which are throv/n off from it. 

* From the Latin incido, to fall upon. 



Light influenced by attraction. Two fundamental principles of optics, 
huf. case a ray of light is said to be reflected.. Incident and reflected rays. 



ANGLES OF INCIDENCE AND REFLECTION. 255 

When a ray of Wght falls perpewiicularly on an opaque 
body, It is reflected back in the same Hne in which it pro- 
ceeded ; in this case the reflected ray returns in the same 
path as that in which the incident ray went. Bat when a 
ray falls obliquely, it is reflected obliquely ; that is, the re- 
flected ray proceeds in a direction on the opposite side, as 
far from the perpendicular as was the incident ray. 

673. The angle made by the incident ray at the surface 
of the reflector, with a line perpendicular to that surface, is 
called the angle of incidence ; the angle made by the re- 
flected ray with the same perpendicular line is called the 

of refection. 

Suppose A B to represent a reflecting 
surface, C D a perpendicular to this sur- 
^\ face, E D the incident, and F D the re- 
\ fleeted ray, the angle E D C is the angle 
^ of incidence, and the angle F D C is the 
angle of reflection. 

674. Tlie angles of incidence and reflection are equal. 
Let a circle be described around the point D as a centre, 
(see preceding figure,) taking D E for a radius, and it will 
be found that equal portions of circumference lie between E 
C and C F ; this proves that the angles E D C and F D C 
are equal. And, again, since A D C is a quadrant, equally 
divided by the line E D, and B D C is a quadrant equally 
divided by F D, it follows that the angle A D E is equal to 

■mmrV, and the angle E D C is equal to F D C. 




m:^ 



Reflection makes objects visible. 



675. It is by the reflection of light that objects are made 
visible ; but light itself, unless it fall directly upon the eye, 
is invisible. If you close a room so that it is dark, except as 
a beam of light entering through a hole in the window shutter 
gives a partial illumination, you may see a bright spot on the 
wall opposite, and may trace the course of the rays of light 
by means of the motes or small particles of dust floating in 
the air. Thus the agent which enables us to see all other 



A ray falling perpendicularly- A rayfallins; obliquely. Angles of incidence 
and reflection. Equality of the angles of incidence and reflection. Objects 
made visible only by the reflection of light. 



-256 NATURAL PHILOSOPHY. 

things, remains itself unseen, and like its great Creator, is 
known to us only by its effects. 

The eye itself is not made sensible of the presence of 
light, till, after a certain series of operations upon its various 
coverings and humours, seeing is produced. 

676. Light is reflected from the various objects with which 
we are surrounded, and by this reflection, images of them 
are formed upon our organs of sight. But smooth and pol- 
ished surfaces reflect light m.ost powerfully, and send to the 
eye the images of the objects from which the light proceeded 
before reflection. Glass, which is transparent, or in other 
words, which transmits ra5's of light, by being rendered 
opaque, is made to reflect them. This is done by a metallic 
covering called an amalgam, applied to one side. This 
amalgam interrupts the light in its passage from the glass 
into the air, turns back the rays, and throws them either di- 
rectly in the incident line, or in an oblique direction. 

677. The reason why trees, rocks and men are not all 
mirrors, reflecting other forms instead of their own, is that 

their surfaces are uneven. — 
Rays of light reflected from un- 
even surfaces are diffused in all 
directions. The parallel, hori- 
zontal lines in the figure, repre- 
sent the sun's rays, v/hich strik- 
ing upon the angular surfaces of 
the body a h, are diffused as 
seen in the dotted lines. 'If- the, 
reflecting surface be polished, 
although uneven, it will be very 
brilliant, as in crystals, diamonds, 
and cut glass. Here the effect is produced by the reflec- 
tion of light from a great many polished angles. 

Mirrors. 

678. A Mirror is a smooth surface which reflects light. 
Thus a still lake, a polished plate of metal, and a looking- 
glass, are mirrors. That department of optics which treats 



Sui-faces which reflect light most powerful!}'. Light reflected from mieven 
surfaces. 




PLANE MIRRORS 



257 



of the reflection of light by means of mirrors, is called 
Catoptrics.* 

Mirrors are of three kinds, the plane, convex, and concave. 

A plane mirror is flat, or has its surface a perfect plane 
as in a common looking-glass. 

A convex mirror is globular, and reflects images from a 
rounded surface. 

A concave mirror is curved inward, and reflects light from 
a hollow surface. 

The Plane Mirror. 

679. A common looking-glass is a plane rairror compos- 
ed of glass rendered opaque, by a coating of tin and mercu- 
ry. Thus after the rays of light have passed through the 
glass, they are thrown back by the metallic surface. The 
glass is only necessary for preserving this surface smooth 
and clear. The rays of light in passing through the glass, 
suffer some degree of refraction, and thus give a less perfect 
image than a pure metallic reflector. For this reason, in ma- 
ny optical glasses, such mirrors are used. The term specu- 
lum is used to describe a reflector which is metallic, or made 
of silver, tin, &c. ; sometimes all mirrors are called specula. 



Fiir. 183. 




680. Parallel rays falling 
ohliquely on a plane mirror are 
reflected parallel ;— thus the rays 
d b, and c a, which are parallel, 
are reflected towards h and k. 

Converging rays are reflect- 
ed from a plane mirror with 
the same degree of conver- 
gence ; dh and c a are con- 
vergent, and without the inter- 
position of the mirror, they 
would unite in the point E, 
but being reflected, they unite 
in the opposite point F. 



A word from the Greek katoptron, a mirror. 



Different kinds of mirrors. Common looking glass. Speculum. Parallel 
rays falling obliquely on a plane mirror. Converging rays reflected from a 
plane mirror. 

22* 



258 



NATURAL PHILOSOPHY. 




Diverging rays are re- 
equally divergent 
from a plane mirror ; d b 
and c a are divergent rays ; 
if they had proceeded with- 
out interruption from the 
mirror, they would not 
have united at any point 
beyond it, as may be seen 
iE •■■* /' at E and F, because the 

tendency of divergent rays 

r/ is to depart slill farther 

from each other, falling upon the surface of the mirror, they 

are reflected towards li and k, the lines of reflection being 

equally divergent with the lines of incidence. 

681. When an object is placed before a plane mirror, an 
image of it is formed, which appears to be as far behind the 
mirror, as the real object is before it. 

pj„. ^;;g Suppose M R to be a marble slab, an 

elastic ball thrown from A, perpendicu- 
^^■■■•- larly towards it, at D would rebound in. 
B^ the same line to A ; but if thrown oblique- 
J. ly as from B to D, it would move off to b, 




I as far on the opposite side of the perpen- 
dicular, making the angle of reflection 
equal to the angle o^ incidence ; if thrown 
iS---" from C, it would be reflected at c ; and 
so from any other point, the same law would govern the re- 
flection. But suppose M R were a plane mirror, and light 
were to pass from an eye situated at A, the eye would see 
itself as if behind the mirror at d; or an eye at b would see 
an object situated at B as if it were at e ; or an eye at c 
would see an object at C as if it vv^ere at /'. The incident 
ray A D, and the reflected ray D d, or the incident ra)'- B, 
and the reflected ray D e, form together what is called the 
passage of reflection, and this will therefore make the 
real distance of an image seen in a plane mirror, to appear 
as far again from the eye as it really is, or in other words, 
the image will appear as far behind the mirror as the real 



Diverging rays reflected from a plane mirror. Apparent situation of 
image fortned by reflection from a plane mirror. Passage of reflection. 



PLANE MIRRORS. 



259 



object is before it. When you stand before a looking glass, 
you see your figure as if behind the glass; if you walk 
towards the glass, the image will approach, but with double 
the real velocity, because both the incident and reflected 
rays are contracted by the movement. If you walk from 
the glass the image seems to retire from you with double 
your own speed. 

682. Any object which reflects 
light is called a radiant. Suppose 
then, A to be a radiant situated before 
the mirror M N. The ray A B fall- 
^ \ ing upon the mirror, is reflected in 
the line B C, let a perpendicular line 
'^ be drawn from A to a, and extend 
-B the reflected ray B C, till it cuts the 
^0^ perpendicular at a, the distance a S is 
""* equal to S A, also every other ray 
proceeding from the radiant A will be 
reflected as if coming from behind the mirror at a. To an 
eye at O, the image a would appear as far behind the mir- 
ror, as the radiant A is before it. 

The point from which rays diverge, or the radiant, is call- 
ed the focus of divergent rays, and the point behind a re- 
flecting surface from which they appear to diverge is called 
the virtual focus. 

683. Since rays of light are reflected at the same angle 
at which they strike a reflecting surface, two persons may 
stand in such positions that each can see the image of the 
other in a mirror, without seeing bis own. Thus, suppose 




Why dues your im.ige seem to move with double yotii' velocity when you 
approacli, oi- recede iVoin a mirror 1 Radiant. Focus of divergent rays. 
Virtual locus. 



260 



NATURAL PHILOSOPHY. 



Pig. 1S8. M N to represent fi mirror, A 

and B the positions of two per- 
9 sons with regard to it ; the dot- 

I ted line P C is a perpendicular 

drawn from the surface of the 
glass at the point P, where tiie 
rays from A and B, fall upon the 
mirror. The person at A, look- 
'Ning towards the mirror, w.ould 
not see his own image, but that 
of him who stood at B, which 
would appear as if behind the 
mirror at b ; in the same man- 
ner B would see A, as if stand- 
ing at a. Thus the image of a person may be seen by re- 
flection from a mirror, wiieo the individual is not conscious 
of being observed. 

684. A person may see the whole of his figure in a plane 




mirror which is but half his height 

Fig. 189. 
^ - A 




Suppose B D to be 
a m.irror half as high 
as the figure at A C ; 
the ray of light A B 
from the eye, falling 
perpendicularly on 
the mirror is reflect- 
ed back in the same line, but the ray C D, from the foot 
which falls obliquely, is reflected in the line D A. Since 
we view objects in the direction of the reflected rays which 
meet the eye, and as the image appears at the same distance 
behind the mirror that the real object is before it, the line 
A D must be extended to E, and the line C D to F, and here 
the image will appear to be situated. 

But if the mirror is less than half the height of the figure, 
the v.'hole of it cannot be reflected. Thus it may be seen in 
the preceding cut, that were the mirror only of the height of 
O B, the line C O from the foot of the figure would be re- 
flected in the line O F, above the eye. 



la what positions may two persons see each other's image in a mirror without 
seeing their own 1 How may one see an image of his whole figure in a mirror 
but half his height.'' Suppose the mirror to be less than half the height of the 
fL":me. 




CONVEX MIRRORS. 2Q1 

085. An object viewed in a mirror appears reversed ; thus 
tiie left foot of the figure A C (see fig. 189) or the one which 
seems stepping forward, appears the right foot in the image F 
E, and when we stretch out our right hand to take that of the 
image in a mirror, the latter seems to offer a left hand. By 
Fig. 190. holding written or printed charac- 

ters before a mirror, we perceive 
very plainly the effect of this rever- 
sion in changing the image of ob- 
jects from right to left. In the hu- 
man figure there is generally great 
uniformity ; the features on one 
side of the face being usually a 
very exact representation of those on the other ; but where 
there is any peculiarity, as the nose a little turned to one 
side, or a squint eye, a man who should undertake to paint 
his own portrait would be in danger of reversing these traits, 
and making a caricature instead of a likeness. By reflect- 
ing an image f\-om one mirror to another, the last reflection 
presents the object without being reversed, and v/ritten or 
prined characters appear as when seen without ^ny reflec- 
tion. 

Convex Mirrors. 

Fig. 191. 686. Convex mirrors reflect light from 

a rounded surface, as A B. Any polish- 
ed convex body is a mirror, as the spheri- 
cal part of brass andirons with which 
children often amuse themselves in view- 
ing their own miniature likenesses. The 
human eye is the most perfect of all convex mirrors, and so 
great is its power of diminishing objects and yet preserving 
their exact likenesses, that on a surface of less than half an 
inch in diameter, may be represented a landscape where 
men, animals and buildings, distant fields and hills, with 
mountains and clouds, are distinctly delineated. 

687. Convex mirrors disperse rays of light ; — they cause 
parallel rays to diverge, diverging rays to diverge raore, and 
converging rays to diverge less. 

Image of objects seen in a reversed position. Whnt is a convex minor ? The 
most perfect convex mirror. Effect of convex mirrors upon liglit. 



262 NATURAL PHILOSOPHY. 

Fiff. 192. 



Nb 

Let M N be a convex mirror, A M and A D and A N 
parallel rays falling upon it ; if the mirror were flat, the 
rays would all be perpendicular to it, bat as it is spherical, no 
ray can be perpendicular to it which is not directed towards 
C, the centre of the sphere. The ray A D is perpendicular 
to the supposed centre, of which the convex mirror forms a 
part. Therefore A D, which falls perpendicularly, is re- 
flected in the same line. But A M and A N, which fall 
obliquely, are reflected obliquely, in the direction M B and 
N B. The dotted lines C E, which meet in the centre of 
the sphere, and are therefore perpendicular* to it, divide the 
angles of incidence and reflection, which may be seen to be 
equal. The image will be seen at F, which is the point 
where the reflected .rays, if continued through the mirror, 
would unite. This point, which is equally distant from the 
surface and centre of the sphere, is called the virtual or 
imaginary focus. 

The axis of a convex mirror, is a line passing through its 
centre, as A C. (See fig. 192.) 

* Any body fallins^ to the earth by the force of gravitation, and therefore mov- 
ing towards the centre in a right lirie, is said to be perpendicular to the centre. 

What r ay can be perpendicular to a convex mirror ? Axis of a convex mirror. 



CONVEX MIRRORS. 



263 




-689. All spherical mirrors are curvilin- 
ear, that is, they are arcs or segments of 
circles. Curves are formed of a number 
of straight lines, or points^ infinitely short, 
and inclining to each other, like the stones in 
the arch of a bridge. Now each of these 
points may be considered as a plane mirror, and the whole 
convex surface as consisting of innumerable small plane mir- 
rors, placed at angles with respect to each other, but forming 
a curve in their general arrangem.ent. Now only such rays 
as fall perpendicularly upon the convex surface, or are direct- 
ed towards its supposed centre, will be reflected back in the 
sam.e direction ; all other parallel rays will fall obliquely 
upon it, and be subject to the general law of reflection; 
viz., that the angles of reflection and incidence are equal. 



F\i. 194. 




690. Suppose the rays a b and 
c d to be parallel, yet falling on the 
convex surface d h, they are, from 
their different points of incidence, 
rendered divergent in h and e, the 
angle of reflection with respect to 
each being equal to the angle of 
incidence. 



691. Again, suppose the 
rays a h and cd to be conver- 
gent ; without the interposi- 
tion of the reflector b d, they 
would unite at m, but they 
now proceed to unite in /, 
which is more distant from 
the reflecting surface than 
the point w ; and it is evi- 
dent that if the curvation of 
the two branches of the re- 
flecting surface b and d was 
greater, they might be re- 
flected parallel or even di- 
veriient. 



spherical mirrdrs curvilinear. Parallel raj-s fallin;. 
Gonverg'.ng rays falling on a convex snvface. 



on a convex surface. 



264 



NATURAL PHILOSOPHY 



Ffe. 196. 




^x 



692. Again, the rays a h and 
c d which without the interposi- 
tion of the convex surface b d, 
would diverge but little atm, be- 
come after reflection, much more 
divergent, as may be seen in the 
space /, and the angles of reflec- 
\^ tion will be found in all these 
i cases exactly equal to the an- 
/ gles of incidence, if measured 
from the reflecting surface pro- 
duced or lengthened as at f g 
and i k. 



693. Convex miri'ors represent objects smaller than they 
are in reality. This is because the angle formed by the re- 
flected ray, called the visual angle, is rendered more acute 
by the convex surface, than by a plane surface. Suppose 
the object C D placed before the convex mirror a b ; the 

Fi^. 197. 




two ra\"s C e and D d, which proceed from the extremities 
of the object, and which if not interrupted by the mirror, 
would converge at^f, are reflected less convergent, and unite 
at ?", forming an angle more acute than if they had not been 
reflected. 

694. Again, objects appear less in a convex mirror, than 

;n a common looking glass, because the convex surface re- 



Diverging rays falling on a convex surface. Vriiy do con" 2 V mirrors rcprc 
sent objects smaller tliau they are in reality 1 



CONVEX MIRRORS. 



265 



fleets rays from points nearer to each other ; " * Suppose 
the straight Hne b d to he a common mirror, the ray from 
the point a, of the object, will be reflected to the eye at e 
from p, and the fay from r will be reflected from q, and the 
image will appear at I M of the same size, as the object would 
appear if viewed from the other side of the glass at o, be- 
Fig. 198. 




cause the angle p e q and the angle p oq are equal. But 
when the same object is reflected from a convex surface, re- 
presented by the curved line, the reflections from the top 
and bottom of it will take place from points nearer than 
before, viz., from n to s» The image is therefore reflected 
from the reduced space of n s, instead of from pq, and it 
will appear consequently, less than the object as at i m. 
The angle subtended to the eye, by the reflection from the 
convex surface, is, you perceive, much less than that of the 
reflection from the plane mirror, and the difference in appa- 
rent size, of the two reflections will bear the same propor- 
tion as the space between p q bears to the space between 
n 5." 



BakewelPs Philosophy. 



23 



266 



NATURAL PHILOSOPHr, 

Fig. 199. 

O 




695. Let the vase A B be placed before the convex mir- 
ror O P, an eye at C would see its miniature image at a h. 
Had the incident rays from A B, the extremities of the vase, 
met with no interruption, they would have converged at D, 
but being reflected from the convex surface, they do not con- 
verge until they reach the point C, more distant from the 
mirror than D. The image being seen under a smaller an- 
gle than the object, appears sm.aller. Objects appear large 
or small according to the breadth of the angle formed by 
rays of light from their extremities. In looking upon a large 
and small tree at equal distances from the eye, the angles made 
by rays of light from the two upper and lower extremities, 
give the idea of their comparative height, for the wider the 
opening of the angle, as it recedes from the eye, the larger 
Fig. 200. 




the object appears. Thus the angle A. B D, being greater 
than the angle B A C, the object A D appears proportiona- 
bly larger than C B. It is the diminishing of the visual an- 
gle by causing rays of light to be farther extended before 



CONYEX MIRRORS. 



267 



tlley'iHeet in a point, which produces the miniature images 
of convex mirrors. 

696. 1. As the visual angle is diminished by distance, 
the farther an object is removed from a convex mirror the 
smaller is the image refected hy it. 

2. Since the different points of an object are not equally 
distant from the surface of a convex mirror, the image will 
appear curved. 

3« As convex mirrors cause rays of light to diverge, ima- 
ges appear nearer the surface of the reflector, than in plane 
mirrors. 

F^g- 201. ^ Let A B be an object 

placed before the convex 
mirror M N, in such a 
position that a reflected 
ray may enter the eye 
placed at H. From C 
draw C A, and C B, inter- 
secting the mirror in E 
and F. The -rays A F 
and A G, will be reflected 
to H and K, and will 
therefore enter the eye as 
if they came from a, at 
the point where the per- 
pendicular A C, is intersected by the dotted lines from _ F 
and G. Likewise B/and B ^ falling upon the points/^, 
will be reflected to the eye as if they came from h, the point 
where they intersect the perpendicular B C. The rays be- 
ing thus rendered more divergent by reflection they appear to 
come from a h nearer to the mirror, than A B, and since the 
extreme points a and h are nearer to each other than A B, 
the image will be represented of less size. 

The greater the convexity of a reflector, the more will the 
images of objects be diminished, and the nearer will they 
appear to the surface. 

697. Concave mirrors furnish science with many curious 
and interesting fticts ; they are used as ornaments for apart- 
ments, and afford much amusement, by their small, and some- 
what distorted imagoes. " Small convex reflectors are made 




Enarnerate three important laws with respect to images formed by convex 
mirrors. Explain figure 201. Use of concave mirrors. 



268 



NATURAL PHILOSOPHY. 



for the use of travellers, who when fatigued by stretching 
the eye to Alps towering on Alps, can, by their mirror, bring 
those sublime objects into a narrow compass, and gratify 
the sight by pictures, which the art of man in vain attempts 
to imitate."* 

Concave Mirrors. 

Pig.202, 698. Concave mirrors reflect light from a holloiv 
surface. The concave mirror being in form, the re- 
^E verse of the convex, we find its powers essentially dif- 
ferent. Convave mirrors collect rays of light, and 
magnify objects, while convex mirrors disperse rays 
of light, and diminish objects, and plane mirrors reflect 
the rays of light, without either enlarging or diminish- 
ff ing the visual angle, and consequently represent ob- 
jects of their natural size. 

699. In a hollow sphere, or part of a 
sphere, with a polished internal surface, if 
rays radiate from the centre in all directions, 
they reach every part perpendicularly, and 
are therefore thrown back to the centre. 
Thus if A B were a concave spherical mir- 
ror, of which C were the centre, rays issuing 
from C would meet again at tise same point. 
700. Concave mirrors jender rays of light more conver- 
gent. 

The surface of a concave mirror, like 
c£ that of a convex mirror, may be consider- 
ed as composed of numbers of points or 
small plane mirrors, but in the concave, 
these points are inclined towards each 
other, while in the convex, they lean in 
the contrary direction. Thus let A B, 
be one section of a concave mirror, and 
c d parallel rays falling upon points on its 
surface, instead of being reflected paral- 
lel, as in the case of a plane mirror, or 





Difference between concave and convex mirrors. Rays radiating from the 
centre of a hollow sphere. How is it proved that concave mirrors render rays 
of light more convergent. 



CONCAVE MIRRORS, 



269 



divergent, as in a convex mirror, they converge and meet in 
the focus e, as they would do in the case of two plane mir- 
rors leaning towards each other and meeting in the point o. 

701. Let A B represent a 



205. 



A y 




-e- 



tre of concavity, or the centre 
of the sphere of which the mir- 
ror is a section. The Ikie F 
—1} C c passing tlifGUgli its centre 

is the axis of the mirror. F, is 

the focus of parallel rays ; or 

""^ that point before the mirror, 

& where the 'parallel rays, a b c 

d and e, being reflected, meet. 

^^""- -•"**' This focus is situated halfway 

between the surface of the mirror S, and the centre of con- 
cavity, C. 

702. Again, let G M represent 
a concave mirror, C being the 
centre of concavity ; the paral- 
lel rays yG and/" M will pass to 
the other side of the perpendicu- 
lars C G and C M, and meet at 
the focus of parallel rays F. 

But when the incident rays are 
divergent, the focus is removed 
farther from ithe surface of the 
mirror. If they diverge from a 
point more remote than the cen- 
tre, as A G and AM, making a 
less angle with the perpendiculars 
than the parallel rays make, they 
will also make a less angle on 
the other side of the perpendicu- 
lars, and meet in the point a be- 
tween the focus and centre. If rays diveige from the cen- 
tre, as C G, C O and C M, they will be reflected back to the 
same point C, because they are all perpendicular to the cen- 
tre. Rays which diverge from a point between the centre 
and a focus, as from a, converge to a point V, on the other 




Rxplain figure 205. Explain figure 20G. 

23* 



270 NATURAL PHILOSOPHY. 

side of the centre. Rays diverging from the focus F are 
reflected parallel as G/and M/'. 

- Rays that approach the mirror converging as (Z G and d M, 
meet in a point, between the focus and the mirror as at D, 
and when rays diverge from D they are reflected in the lines 
G d and M d, appearing to proceed from the point V behind 
the mirror, which point is called the virtual or imaginary 
focus. 

703. «' One who looks into a concave mirror, sees his own 
face varied in the following manner. When he holds the 
reflector near his face, he sees his image distinct, because 
the rays come to the eye diverging, (which is their natural 
state with respect to near objects) and enlarged, because as 
the rays diverge less than before, the image is thrown back 
to a greater distance behind the mirror, than the object is 
before it, and the magnitude is proportioned to that distance* 
As he withdraws the eye, the image grows larger and larger 
until the eye reaches the focus. From the focus to the cen- 
tre no distinct image is seen, because the rays come to the 
eye converging, a condition incompatible with distinct vision. 
At the centre the eye sees only its own image, since the 
image is reflected back to the object, and coincides with it. 
Beyond the centre his face will be seen, on the other side of 
the centre before the mirror, (though liabit may lead him to 
refer it to a point behind it,) and it will be diminished, being 
nearer to the mirror than the object is, and inverted, bcause 
an mverted image is formed when the rays are brought to a 
focus, and this becomes the object which is seen by the 
eye."* 

704. The sun''s rays, on account of the vast distance of 
that body from the earth, are considered as parallel ; they 
converge to a point, as the focus of parallel rays in concave 
reflectors. Even in so small and imperfect a reflector as a 
watch glass, the focal point may, from the concentrated rays 
of the sun, become heated to such a degree as to inflame 
combustibles. Thus watch glasses are sometimes used to 

' Olmsted. 

How may a person, vicvring' his image m a concave mirror, vary tbis imsge 
by a cliange of position .^ Heat produced by concentrating solar rays in small 
reflectors. 



CONCAVE MIRRORS. 271 

light tobacco pipes and kindle fires. The word focus ori- 
ginally signified the burning point, or fire-place. The 
greater the concave surface, and the more perfect the re^ 
fleeter, the more powerful will be its effect in concentrating 
the solar rays. Metallic concave mirrors have been manu- 
factured four or five feet in diameter ; they are called burn- 
ing mirrors. The heat at the focus of such mirrors is suffi» 
ciently pov/erful to fuse metals, and even earths. The phi- 
losopher A.rchimedes, is said to have set fire to the Roman 
fleet under Marcellus, by means of a huge burning mirror. 
He must have placed it in such a position that the con- 
centrated solar rays were reflected directly upon the ships of 
the enemy. 

705. It has been shown that when the incident rays are 
parallel, the reflected rays converge to a focus. On the 
contrary, when the incident rays proceed from a focus, or 
are divergent, they are reflected parallel ; thus let a burning 
taper be placed in the focus of a concave mirror ; the ray 
which falls in the direction of the axis of the mirror, is re- 
Fig- 207. fleeted back in the same linoj 

but the rays which fall at B 
and F are reflected to A and 
K, the dotted lines being the 
perpendiculars which sepa= 
rate the lines of incidence 
and reflection, and shew their 
angles to be equal. Or, in 
other words, the divergent 
rays, B and F, are reflected 
parallel. This dispersing of divergent rays, is the reverse 
of collecting parallel rays into a focus, as is done by means 
of burning glasses. 

706. It is only when an object is nearer to a concave 
mirror than its centre of concavity, that its image is magni- 
fied ; for when the object is farther from the mirror, this 
Centre will appear less than the object, and in an inverted 
position. Suppose a. person. A, stand before a coilcave mir- 
ror below its axis a c, and beyond its centre of concavity Co 
A ray of light b a, proceeding from the feet would fall upon 

Moaning of the vyoid focus. Burning minors. Dispersion of divergent raj^;. 




^2 



NATURAL PHILOSOPHY. 

Fig. 208. 




the mirror at a, and be reflected to e, on the opposite side, at 
an equal angle from the axis a c. The rays h e and h d, 
also proceeding from the feet, are reflected in the lines e i 
and d i, and an image of the feet appears at i. The rays 
from the head of the person diverging in like manner in all 
directions, proceed to the points e and d, from whence they 
are reflected in the dotted lines to 7n, where appears an image 
of the head. Rays proceeding from other parts of the body, 
will also be reflected in their proper positions between m 
and i, where an inverted and diminished imag^e of the 
whole figure appears. This image fc beyond the focus 
f of parallel rays, because of the diverging of the incident 
rays, and the greater this diverging the more distant will be 
the image from that focus. " Thus if a man place himself 
directly before a large concave mirror, but farther from it 
than its centre of concavity, he will see an inverted image of 
himself in the air between him and the mirror, of a less size 
than himself, and if he hold out his hand towards the mirror, 
the hand of the image will come out towards his hand, and 
coincide with it, of an equal bulk when his hand is in the 
centre of concavity, and he will imagine he may shake hands" 
with his image. If he reach his hand furdier, the hand of 
the image will pass by his hand, and come between it and 
his body ; and if he move his hand towards either side, 
the hand of the image will move towards the other, so that 
whatever way the object moves, the image will move the 
contrary way. This appearance of the image in the air be- 
tween the mirror and the object, has been productive of many 
deceptions, which when exhibited with art, and an air oi 

Explain figure 208= 



CONCAVE MIRRORS. 273 

mystery, have been a source of gain to public show-meno 
The images of objects have been exhibited in this manner so 
as to surprise the ignorant, and please the scientific."* 

707. When we consider the various appearances produ- 
ced by the reflection of light from plane, convex and con- 
cave mirrors, we need not be surprised that advantage has 
been taken of these natural phenomena by artful men to im- 
pose on the credulous. Kings and priests in ancient days 
maintained their authority over the persons and minds of 
mankind by operating on their superstitious fears. In the 
dark ages, monasteries, so far from being asylums !for 
holy meditation, and pious devotion, were theatres for the 
exercise of diabolical plans to enslave the human mind by 
pretended miracles and supernatural apparitions. Priests, 
who were alchymists and opticians, abused their knowledge 
of nature, for the purpose of darkening and bewildering hu» 
man intellect. " The concave mirror,'^ says Brewster, " is 
the staple instrument of the magician's cabinet, and must al- 
ways perform a principal part in all optical deceptions. It 
can scarcely be doubted that a concave mirror was the 
principle instrument by which the heathen gods were made 
to appear in the ancient temples. In the temple of Hercules 
at Tyre, Pliny mentions that there was a seat made of con^ 
secrated stone, 'from which the gods easily rose.' In order 
to heighten the illusion, intended to be produced by exhibi- 
tions of objects by reflection from a concave mirror, a great 
variety of expedients are resorted to ; among others, is that 
of a concealed chafing-dish, from which issues wreaths of 
smoke from burning perfumes, enveloping the figure and 
thus causing it to appear as if suspended in the clouds. Len- 
ses of various kinds may be so placed as to represent an 
erect, instead of an inverted image, of the reflected object. 
Imagine a room in the darkness and stillness of midnight, 
suddenly to appear illuminated by means of some concealed 
opening in the ceiling, and a superstitious monk or trembling 
novice, to see suspended in the clouds, some fearful object, 
illuminated words, a drawn dagger or a cloven foot ! — artful 
priests following up such impositions by threatenings and 

" Imison's Elements. 

Imposilions practiced by means of optical phenomena. 



274 NATURAL PHILOSOPHY. 

persuasions, thus gain an entire ascendency over the helpless 
and deluded being, who, ignorant of any natural means by 
which such phenomena could be produced, believes that the 
Almighty has supernaturally warned or threatened him, and 
that his only safety consists in yielding himself up, soul and 
body, to the apparently holy men, who so zealously proffer 
their services. Can we too much rejoice in the emancipa- 
tion of the human mind, from mtellectual bondage, or too 
much praise the efforts now made by men of science, the 
priests of nature, to diffuse the knowledge of her laws, and 
unveil the mysteries in which she was for so many ages 
shrouded ! Religion, too, released from the embrace of su- 
perstition and deceit, which, serpent-like, would have stran- 
gled her in their grasp, now goes forth in her own strength 
and beautiful simplicity, calling on man to 'praise God for 
his wonderful works,' and adding to the human soul that vi- 
tal spark of pietv, without which, philosophy is cold and 
lifeless." 



LECTURE XXXIY 



REFRACTION OF LIGHT. 

703. We have considered the various ways in Vv'hich light 
is reflected by opaque bodies, plane, convex and concave ; 
we now pass on to the subject o^ refraction, in which we are 
to examine the manner in which light passes through trans- 
parent bodies. 

A ray of light at E C, falling through air perpendicular- 
ly, upon a surface of glass or water k. B, passes on in a 

Light passing through transparent bodies of different densities. 



REFRACTION OP LIGHT. 



27^5 




209. 

E 




straight line through 
the body to F ; hut if 
a ray in passing from 
one medium into anoth. 
er of dijferent densi- 
ty, fall obliquely as D 

^ \JC -p h, it is hent from its 

straight course, which 
would he in the direc 
Hon D K, and recedes 
P from it, either towards 
L or O, and this bend- 
ing is called refrac- 
tion. 

709. If light pass from a rarer into a denser medium, it 
is refracted towards a perpendicular in that medium. 

p,^ 2^(^ Suppose the ray C B to pass 

I obliquely from air into a den- 
Is er medium, water. The course 
I of this ray through the air 
1 would be in the direction C B 
, D, but as soon as it enters the 
' water, it is bent towards the 
perpendicular ABE, and 
moves on towards F in the di- 
rection between B D and B E^ 
making a less angle with the 
Ji: iP B perpendicular, than if it had 

suffered no refraction. 

710. If light pass from a denser into a rarer medium, it 
is refracted farther from a perpendicular in that medium. 

Letj the upper and more shaded part of the figure repre. 
sent glass, and the lower part, a rarer medium, viz., water ; 



Light passing from a rarer into a denser medium. 



276 



NATURAL PHILOSOPHY, 



and let C B be a ray pas- 
sing obliquely from the glass 
into water ; on arriving at the 
surface of the rarer medium 
the ray does not pass on in 
a straight line towards F, but 
is bent from the perpendicular 
B E in the line B D, mak- 
ing a greater angle with the 

perpendicular than if it had 

^^P suffered no refraction. 

As it is important that this 
subject with the different terms 
employed in treating of it, 
should be well understood, we 
will add another figure by way 
of illustration. Let A B rep- 
resent the surface which sepa- 
rates the two mediums, that 
from which the ray comes, and 
that into which it enters, this' 
is called the refracting surf ace. 
The ray P C which falls upon 
it, is called the incident ray, and the ray C R or C S is call- 
ed the broken or refracted ray ; and this, as we have be- 
fore shewn, varies from the perpendicular E C F, according 
as the refracting medium is more or less dense. The angle 
formed by the incident ray P C, with the perpendicular E 
C, that is, the angle P C E, is called the angle of incidence, 
and the angles formed by the refracted ray C R or C S with 
the perpendicular C F, that is the angle F C R or F C S, are 
called angles of refraction. On account of the bending 
which the ray of light undergoes, the angles of refraction 
and incidence are never equal.? . 

* This is proved by a reference to gerometry ; thus, producing the line P C to 
<&,<Seefig. 212.) the angles Q, C Rjbeing vertical, areequal to each other accord- 
ing to the loth problem of Euclid'/lst. Book. The angle Q, C F then, is equal 
to the angle of incidence P C E ; therefore the angle of refraction R C F or S C F. 

* See Euler's Letters. Harper's Ed. Vol. I. page 120. 




Litfht passing from a denser into a rarer medium. Explain figure 212. An- 
gles of incidence and refraction never equal. 



REFRACTIVE POWERS OP BODIES. 



277 



Bijferent Refractive Powers of Bodies, 

711. Transparent bodies differ in their power of bending 
light ; — as a general rule, the refractive power is propor- 
tioned to the density. Thus, the refractive power of water 
is greater than that of air; the refractive power of glass 
is greater than that of water, and the refractive power of the 
diamond is greater than all. 

712. But the chemical constitution of bodies, as well as 
their density, is found to affect their refracting power. 
Newton first discovered that inflammable bodies possess this 
power in a high degree, and he even ventured to predict that 
water and diamond might have in their composition inflam- 
mable matter. This hypothesis, which appeared so vision, 
ary, at that day, has been proved by chemistry in the most 
satisfactory manner. Hydrogen, one of the constituents of 
water, is now known as one of the most combustible of all 
substances ;and diamond, which is crystallised carbon, may 
be burned like charcoal. 

71?'. Suppose a ray of 
light, A P,to pass into water. 
Instead of proceeding in a 
straight line to O, it will 
be bent in the line P D. If, 
instead of water,the refrac- 
ting medium be sulphur, 
a denser and more inflam- 
mable substance, the ray 
v/ill be bent in the line P 
F. If the medium be dia- 
mond, the refraction will 

„ Water ^^ ^'^ ^^^® ^^"® ^ ^' "^^^ 

ISuJ/ilie?^ angle at which water is 

'nca9no?id refracted, that is the angle 



213. 




is greater or less. There are tlicn only two cases which can exist; the ont% 
in which the refracted ray, being C R, t'he angle of refraction R C F is less than 
the angle of incidence P C E ; and tlie other, in wliich the refracted ray being C 
S, theangliof rcfraclion is greater than the angle ofini'idencc PC E. In the 
former case, we say that the'i-ay C R approaches the p.-rpcndicular, C P ;_ and in 
the other, that the refracted ray, C S recedes or diviates li 



the 



p,>:ri 



lendiciilai 



Bodies differ in their refractive powers. The roh active powers of bodies af- 
fected by their chemical constitution. Conibiistiblo substances proved to possess 
most rcf>'active power. 

24 



2f8 NATURAL PHILOSOPHY. 

O P M, will be seen to be the greatest, and the angle at 
which diamond is refracted, or the angle fl P M, the 
smallest. 

The angle of incidence, or the angle A P L, does not vary- 
in the different cases of refraction represented in the figure. 

Let a line A B, (fig. 213.) be drawn at the shortest dis- 
tance of the point A from the perpendicular L P, this is the 
sine of the angle of incidence. In the same manner is found 
ihe sine D C of the angle of the refraction of water ; the sine 
E F of the refraction of sulphur, and the sine ^ H of the re- 
fraction of diamond. 

714. It has been ascertained from many observations, that 
the sines of the angles of incidence and refraction are always 
in the same ratio ; thus, from air into water, the sine of the 
angle of incidence is to the sine of the angle of refi-action 
nearly as 4 to 3, whatever, be the position of the ray with 
respect to the refracting surface. From air into sulphuT, 
the. sine of the angle of incidence is to the sine of the angle 
of refraction as 2 to 1 ; from air into diamond as 1 to 2-5. 

715, When a ray of light passes from a denser into a 
rarer medium, as from water into air, it is bent /ro;?i the per- 
pendicular ; and the same constant ratio is found to exist 
between the sines of the angles of incidence and refraction. 

p;^ 214 ^^^ A C be the ray incident upon^ 

-^..^^ the rarer medium R, S. It will be 

^v refracted from the perpendicular D 

\ F into the direction C E, so that 
\ the sine A I) is to E F in a con> 

.jg stant ratio. 

^v:::;--^.^^ / A ray of light cannot be refract- 
....^H^yjn Q^^ whenever the sine of the angle 
/ of refraction becomes equal to the 
..^ radius of a circle. Thus in tiie 

preceding figure, if we increase the angle A C D, the angle 
F C E will be also increased, till the lines C E and F E co- 
incide with, or fall upon the radius C S. But if beyond this 
position of the ray A C, the angle A C D is still farther in- 
creased, it is manifest that its sine also is increased ; 
and consequently, in order that the ratio betvreen the sines 
may be constant, the sine of refraction E F, must also be 
increased, Vy-hich is impossible, since we have already sup- 
posed it equal to the radius C S. 

The sines of the angles of incidence and refraction in the same ratio. 



EXAMPLES OP REFRACTION. 279 

716. Thus light falling very obliquely upon a transparent 
medium ceases to be refracted ; but the incident rays are all 
rejiected. This is called total rejiectton. Since the bright- 
ness of the reflected image depends upon the quantity of 
lightj and in ordinary cases of reflection a portion of light is 
absorbed by the reflecting substance, those images which 
arise from total reflection are by far the most vivid, rv 

Familiar Examples of Bef Taction. 

717. 1. An oar with one end in water appears bent, and also 
somewhat shorter than it really is. The rays of hght from 
the immersed part of the oar, proceeding from a denser to a 
rarer medium, are refracted jTrom the perpendicular, and are 
inclined towards the eye of the spectator. Let am a repre- 

Pig. 215. seiit an oar, the part m o being 

out of the water, and the part 
7/1 a in the water ; the rays di- 
verging from a, will appear to 
diverge from h, neaier to the 
surface of the water ; every 
loint in m a will seem nearer to 
the suiTace than it is in reality, and the part of the oar at 
m a will appear to make an angle with the part m o. 

2. The bottom of a river when viewed obliquely ap- 
pears nearer to the eye than it actually is ; for this reason 
the water does not seem as deep as it is in reality. Persons 
in bathing are sometimes thus deceived, and lose their lives 
in consequence of venturing in water beyond their depth. 

3. When we look from a boat perpendicularly into the 
water of a river, we see the bottom in its true place, because 
there is no refraction. But the more obliquely we view an 
object seen through a transparent medium, the more its po- 
sition seems changed. 

4. Take a cup which has the picture of a flower (or other 
figure) at the bottom, and hold it in such a position that the 
object is not visible to the eye at A, being just concealed by 
the top of the cup ; let the cup be filled with water and the 

Total reflection. V/hy does an oar appear bent in water ? Why does a river, 
under certain ciicnnistnnces, appear nioie' shallow than it is 7 Diflerent ajipoar- 
ancc of the bottom of a river when viewed perpendicularly and obliqueI3^ Ex- 
ample of an object at Ihe bottoniof a cii]), seen through water. 





380 NATURAL PHILOSOPHY. 

flower will row be seen witl 9ut 
any change in the position of the 
eye or of the cup. That is, you 
will see the hnage of the flower 
J3 from the point B, although the 
real object is at C. 

5. A goid-fish,. in a glass 
globe filled with water, may ap- 
pear as two fishes, being seen both by light bent through the 
surfcce of the water, and by straight or perpendicular rays 
passing through the sides of the glass. In order to see bodies 
under water in their true places, and in their true propor- 
tions, the eye should view them through a tube, the farther 
end being closed by a plate of glass, and held in the 
water. 

Effects of the Refraction of the Atmosphere. 

718. The atmosphere is a transparent body, becoming 
more dense in proportion as it is nearer the surface of tiie 
eaith. The cUJfereni strata of air having different degrees 
of density, vary in their refractive powers. In considering 
the subject of Acoustics we found the atmosphere to be the 
great conducting medium by which sound is propagated. 
This medium has a no less important effect on light, in its 
transmission, refraction, d^ud decomposition. 

719. The heavenly bodies appear higher than they real- 
ly are, because the rays of light, instead of moving through 
the atmosphere in straight lines, are continually bent towards 
the earth, in consequence of meeting with different mediums 
which become denser, as they are nearer to the earth. If 
is- supposed, that beyond the atmosphere v/hich surrounds 
our globe, there is, if not a vacuum, an atmosphere of a 
highly rarefied nature, called ether. It is proved that 
the refractive power of the earth is greatest at its surface, 
and diminishes upwards. 

The figure represents the difference in the real and ajjpa. 
rewi situation of the star A. R.ays of light falling thus 



Gold- fish in a glass globe. Different refractive powers of atmospheric strata. 
In what respects the atmosphere affects light. Why the heavenly bodies appea/ 
higlier than they really are. 



REFRACTION OF THE ATMOSPHERE. 



281 



Flgr. 217. 




obliquely on the earth, would be re- 
fracted in a curve, as in the line A B, 
and seen in the direction of a tangent 
to that part of the curve which meets 
the eye, B C. Thus, the apparent alti- 
tude is C B, while the real altitude is 
A B. The distance between A and C 
is called the parallax, and is of great 
importance in astronomical calculations. ^ 

It is owing to their parallax that the moon and stars appear 
above the horizon before they have actually risen, and are seen 
after they have set. The day is also lengthened from this cause ; 
for while the sun is yet below the eastern horizon, he is visible by 
means of his refracted rays, and his light lingers some moments 
after he has sunk beneath the western horizon. 

Fig. 218. 720. SupposeEFB 

Ig'i to represent the earth's 
^,in? surface, and C D A the 
atmosphere. The sun 
^^1,,^^ at S would appear to a 
■||| spectator at O as if situ- 
>^ atedatC. The distance 
E / ^" A^i"^ '^^^'^etween the real and 

apparent situation of the sun would lessen until the sun should be in 
the zenith, or directly over the observer ; vv^hen, as the rays fall 
perpendicularly, there would be no 'm^mi^m. The stratum of air 
which the sun's rays must penetrate, in the horizon, is so^ much 
thicker and denser than in the zenith, that the light is diminished 
more than 1300 times in passing through it. It is this that renders 
the rays of the sun, at his rising and setting, so much less dazzhng 
to the eye tlian when he is vertical. 

721. "The loss of light and consequently of heat by the ab-^ 
sorbing power of the atmosphere, increases with the obliquity ot 
incidence. Of ten thousand rays falling on its snrface, 8123 ar- 
rive at a given point of the earth if they fall perpendicularly ; 7024 
arrive if the angle of direction be fifly degrees; 2831 if it be 
seven degrees ; and only five rays will arrive through a hori- 
zontal stratum. Since so great a quantity of light is lost in passing 
through the atmosphere, many celestial objects may be altogether 
invisible from the plain, which may be seen from elevated situa- 
tions. Diminished splendour, and the false estimate we make of 




Real and apparent situation of a star. Parallax. Eftects of the parallax of ibe ce- 
lestial bodies. Explain the effect of the atmosphere upon the sun's rays. >Vhat. effect 
has obliquity of incidence upon polar light andlieat'] 

24* 



282 NATURAL PHILOSOPHY. 

distance, from the number of intervening objects, lead us to sup- 
pose the sun and moon to be much larger when in the horizon than 
at any other altitude, though their apparent diameters are then some- 
what less. Instead of a sudden transition from light to darkness, the 
reflective power of the air adorns nature with the rosy and golden 
hues of the aurora and twilight. Even when the sun is eighteen 
degrees below the horizon, a suuicient portion of light remains to 
shew that, a.t the height of thirty miles, it is still dense enough to 
reflect light. The atmosphere scatters the sun's rays, and gives 
all the beautiful tints and cheerfulness of day. It transmits the 
blue light in the greatest abundance ; the higher we ascend, the 
sky assumes a deeper hue, but in the expanse of space, the sun 
and stars must appear like brilliant specks in the profound black- 
ness."* 

Singular appearances caused hy unusual refraction, or ly total 
reflection. 

722. By unusual, or extraordinai^y refraction, is meant certain 
phenomena which appear to be caused by the unequal density of 
different portions of the atmosphere. We have shewn that the in- 
cident ra}^, by falling very obliquely, causes total reflection instead 
of refraction. Both these causes may be concerned in the produc- 
tion of certain appearances, which in a less philosophical age were 
regarded as the effect of magic. 

723. The elevation of coasts, ships, and mountains, above their 
usual level, when seen in the distant horizon, is called horning. 
The French have given to the same class of phenomena, the name 
Q^ mirage ; and the Italians, who are not unaccustomed to them in 
the Straits of Messina, call them the Fata Morgana. 

When the rising sun throws his rays at an angle of 45° on the 
sea ofReggio, and the water injhe bay is calm and unruffled, a 
spectator on an eminence in the city, v/ho places his back to the 
sun and his face to the sea, sees as if upon tlie surface of the wa- 
ter, castles, arches, columjns and towers, palaces and churches, with 
balconies and domes ; vallies and plains covered with herds and 
flocks ; men walking and riding, and a variety of strange and gro- 
tesque figures, rapidly succeeding each other. AVhen the atmos- 
phere is charged with vapours and exhalations to the height of 
about twenty feet, the same objects, with less distinctness of out- 
line will appear in the mists and vapours floating in the atmos- 

* Mr?. Somerville. "Connection of The Physical Sciences." 

Why do the sun and moon appear largest at the horizon ? Probable appearance of 
the sun and stars beyond the earth's atmosphere. Meaning of unusnal refraction, 
Looming, Mirage, &c, A cily seen upon the surface of water and in the clouds. 



^RIAL IMAGES. 



283 



phere, as if suspended there. If the air be only sufficiently charg- 
ed with moisture to form the rainbow, the objects appear at the 
surface of the sea, and brilliantly fringed with the prismatic 
colours. 

This aerial representation of the objects on the opposite coast, 
as first described by an Italian, in 1793, was scarcely credited, 
until subsequent statements shewed that others had observed simi. 
lar appearances. 

Pi,^ 219. ''24. In 1798, at Ramsgate, a ship was ob- 

served, which appeared as at A, the top-mast 
being the only part which was seen above the 
horizon. An inverted image was seen at B 
just above the real ship^A, and an erect image 
at C. The sea was seen as at V W. As the 
ship A rose to the horizon,* the image C grad- 
ually disappeared, and the image B descended 
towards A. After the v/hole ship was above 
the horizon, the two images B and C were dis. 
tinctly seen. 

725. Captain Scoresby, in a voyage per- 
formed in 1822, knew his fathei-'s ship by its 
inverted image in the air, when the ship itself 
was below the horizon, or entirely out of sight. 
To use his own words, " It was so well defin- 
ed that I could distinguish by a telescope, every 
sail, the general rig of the ship, and its parti- 
cular character, so that I confidently pronoun- 
ced it my father's ship the Fame, which it afterwards proved to be, 
though in comparing notes with my fither, I found that he was 
about 30 miles distant, and seventeen miles beyond the horizon." 

726. The annexed figure with its explanation may serve as an 
illustration of the examples v/e have given of unusual refraction. 

" Let S F be a ship in the horizon, and visible to the eye at E, 
by rays S E, F E proceeding in straight lines to E, through a 
tract of the atmosphere in its usual state. If we suppose (what is 
known to be sometimes the case) that the refractive power of the 
atmosphere, or air, above the line S a E varies, so as to be less at 
c than at a, then rays ^d,¥ c proceeding upwards from tha ship, 
and that never could, in the ordinary state of the air, reach the 
eye at E, will be refracted into curve lines F c, ^ d ; and if the 





* The pupil will recollect that owing to the rotundit}'- of the i artb, tlie top of an ap- 
reaching shij) at sea is the pert lirstscon. 



Aerial representation of a shi'i). Tlie shin Fame known by its aerial image. 



284 NATURAL PHILOSOPHY. 

Fig. 220. 




F 

variation of refractive power is such, that these last ra3's cross 
each other at a:, then the ray S d, in place of being the uppermost, 
will now be the undermost, and, consequently, will enter the eye 
as if it came from the lower end of the object. 

If we now draw lines E 5, E P, tangents to tliese curve lines at 
E, these lines Vv'ill be the direction in which the ship will be seen 
by the rays F c, S d, and the observer at E will see an inverted 
image P .9 of the ship S F considerably elevated above the hori- 
zon. The refractive power of the air still continuing to diminish, 
other rays, S n, F m, tliat never could reach the eye at E in the 
ordinary state of the atmosphere, may likewise be bent into curves 
which will not cross each other before they reach the eye at E. 
In this case, the tangent K Z, to the upper curve S n E will be up- 
permost, and the tangent E D, to the lower curve F m E, lower- 
m.ost, so that the observer at E will see the erect image D I, of 
the ship above the inverted image. It is possible that a third, 
and even a fourth image may be seen. 

727. " If the variation of refractive power takes place only in 
the tract of air through which the rays F c, S ^, pass, then thei*e 
may only be an inverted image ; and if it takes place only in the 
tract through which F ??i, S n pass, there may be only an erect 
image. It is also obvious, that if the variation of refractive power 
commences at the line joining the eye and the horizon, the ordina- 
ry image S F, will not be seen ; and in like manner it is clear that 
the inverted and erect images 5 P, D /, may be seen even if the 
real ship S F is below the visible horizon."* 

728. The mirage is common in hot climates on sandy plains. 
In the middle of the day when the sun shines on the level surface 

' Treatise on Optics — Library of Useful Knowledge. 
Deceptive appearances by means of the mirage. 



MIRAGE. 2SS 

of the sand, the appearance of a sheet of water is observed at a 
little distance ; and so complete is the deception, that any per- 
son ignorant of the cause, would not doubt but he was approach- 
ing a lake or river. This spectral body of water reflects the ani- 
mafs, trees or mountains around, with great distinctness. As the 
traveller, perhaps fainting with thirst, advances, the tantalizing 
phantom of water recedes, exhibiting on its surface new images of 
surrounding objects, A traveller in India thus describes a phe- 
nomenon of this kind. " A deep precipitous valley below us, at 
the bottom of v/hich I had seen one or two miserable villages in 
the morning, bore, in the evening, a complete resemblance to a 
beautiful lake ; the vapour which played the part of water, as- 
cending nearly halfway up the sides of the vale, and on its bright 
surface trees and rocks were distinctly reflected." 

729. Some writers attribute the mirage chiefly to partial, or 
total reflection of the rays of light at thiO surfaces of atmos- 
pheric strata of different densities. The following occurrence 
which happened, in November, 1804, is supposed to have been 
produced by a similar cause. "Dr. Buchan, while watching the 
rising sun from the cliff about a mile to the east of Brighton (Eng- 
land.) at the instant the solar disk, emerged from the surface of 
the ocean, saw the cliff on which he was standing, a wind-mill, his 
own figure, and that of a friend, depicted immediately opposite to 
him, on the sea. This appearance lasted about ten minutes, till 
the sun had risen nearly his own diameter above the surface of 
the waves. The whole then seemed to be elevated into the air 
and successively vanished. The rays of the sun fell upon the 
cliff at an incidence of 73° from the perpendicular, and the sea was 
covered with a dense fog many yards in height, which gradually 
receded from the rising sun." 

730. Dr. Wollaston has proved, by simple experiments, that 
the appearance of double images is owing to the refraction of rays 
through mediums of different densities. 

Ex. If you pour some spirits of wine or alcohol in a bottle con- 
taining water, the spirits of wine, unless the water is agitated, will 
remain in a distinct stratum at the top ; by looking at any object 
behind the bottle, or through these mixed strata, an inverted image 
of the object will appear. Syrup is more dense than water, there- 
fore the same effect will be produced by looking at an object 
through strata of syrup and water. Dr. Wollaston poured into a 
square phial a small quantity of clear syrup, and above this he 

Mirage described by a traveller in India, Supposed cause ot" Uie mirage. Appeuran- 
ces witnessed b}' Dr. Buchan at Brighton. Experinieuts by Dr. Wollaston with refract- 
ing mediums of dilTerent densities. 



286 



NATURAL PHILOSOPHY. 




swfdt 



wof&r 

BUTJW 



poured an equal quantity oi water, which gradu- 
ally combined with the syrup, as seen at A. The 
word Syrup upon a card held behind the bottle, 
appeared erect when seen througii the pure syr- 
up, but inverted, as represented in the figure, 
when seen through the mixture of water and syr- 
up. Dr. Wollaston then put nearly the same 
quantity of rectified spirit of icine above the iva- 
ter, as in the figure at B, and he saw the appear- 
ance there represented, the true place of the 
word Spirit, and the inverted and erect images 
below. By looking along a red hot poker at a 
distant object, an erect and an inverted image is seen. This is in 
consequence of the change produced in the density of the air by 
the heat. The air nearest the heated poker being most rare, its 
refractive power is least. 

781. " We have no doubt," says an English writer, "that some 
of the facts ascribed in the Western Highlands of Scotland to 
second sight, have been owing to the unusual refraction of the at- 
mosphere, and that the same cause will explain some of those won- 
ders vv^hich sceptics discredit, and which superstitious minds attri- 
bute to supernatural causes. The beacon-keeper of the Isle of 
France, v/ho saw ships in the air before they rose above the visi- 
bie horizon, may no'.v recover his good character in the eyes of 
the former, while the latter may cease to regard him as a magi- 
cian." Our country has its superstitious legends of wonderful 
sights, attested by veritable witnesses. The Phantom Ship of the 
Puritans, and the Flying Dutchman of the settlers of New Amster- 
dam, were probably real apparitions, for we find that unequal re- 
fraction may cause a ship to appear as if suspended in the clojds, 
or produce the phantom of a ship, while the real object is cu! of 
sight. 



LECTURE XXXV. 



LEXSES. 



TS2. The substance most used for refracting the rays of light in 
optical experiments, and for optical instruments, is glass in various 
forms, the most common of which are here represented- 

Strange appearances accounted for. 



LENSES. 



287 





Fig. 222. 


5" 


3 C I) E F G H 

I0OPMI 



1. An optical prism, A, is a solid, having two plane surfaces A 
R, A S, inclined to one anotiier, tliese are called its refracting sur- 
faces. 

2. A pZane glass, B, has two plane surfaces parallel to one 
another. 

3. A sphere or spherical lens, C, has every point in its surfice 
equally distant from a common centre, O. 

4. A double convex lens, D, is 
bounded by two convex spherical 
surfiices, whose centres are on oppo= 
site sides of the lens. When the ra- 
p^ s dii of its two surfaces are equal, it 

is said to be equally convex ; and when the radii are unequal, it is 
said to be unequally convex. 

5. A plano-convex lens, E, is bounded by a plane surflice on 
one side, and by a convex one on the other. 

6. A doulle concave lens, F, is bounded by concave surfaces 
on both sides. 

7,1 A plano-concave lens, G, is bounded by a plane surface on 
one side, and a concave on the other. 

8. A meniscus, H, is bounded by a concave and a convex 
spherical surface ; and these two surfaces meet if continued. 

9. A concavo-convex lens, I, is bounded by a concave and a 
convex surface ; but these two surfaces do not meet though con- 
tinued. 

The axis of these lenses is a straight line, M N, in which are 
situated the centres of their spherical surfaces, and to which their 
plane surfaces are perpendicular. 

Fig. 223. 733, The most simple case of re- 

fraction is when the refracting sub- 
stance is terminated by plane surfa- 
ces, parallel to each other. Sup= 
pose M N to be a piece of glass ter. 
xm'nated by plane surfaces, and 
that the ray A C falls obliquely at 
the point C. On entering the glass, 
or proceeding from a rarer to a den- 
ser medium, the direction of the ]-ay 
will be bent out of the straight line 
D/ /E i C D in which it would have moved 

but for the intercepting medium, and will move tov^'ards the per- 
pendicular O P through the glass in the line C c. On leaving th.o 




U 




Piiscuuid Icuscs. Axis of lonsos. C.i 
\?, t imiiiuted by plane, }.'ariillel siaTaCCS. 



ISC of rcfiaclion u!;cn the i\MVaotii 



'^f^ 



NATURAL PHILOSOPHY. 



glass, that is, on going from a denser to a rarer medium, the ray is 
again refracted, but in a contrary direction ; or from the perpendi- 
cular O P towards D. A ray therefore passing obliquely through 
a transparent body of parallel surfa<3es, has its course turned from 
the original direction, but after refraction proceeds in a line parallel 
with that direction, thus E e is parallel with h D. 

734. This refraction takes place in the hght which passes 
through glass windows ; but o\ving to the thinness of the panes, 
the ajpimrent, varies little from the /n^e situation of the objects thus 
seen. When the tvro surfaces of a pane of window glass are not 
planes, or are not perfectly parallel to each other, objects seen 
through it appear more or less distorted. 

735. A Ze?i.5* is usually of glass, ground into such a form as to 
collector disperse the rays of liglrt which pass through it. 

A convex lens collects raj^s of light. A concave lens disperses 
rays of light. 

The sphei'e of a lens is an imaginary 
circle of which its surface is a portion. 
Thus the circle A B C is the sphere of 
the convex lens D. 

The radius of a lens is 'the radius of 
|e its sphere, as D E ; and a line D d pass- 
ing through its centre, is its axis. 

736. The focus is that point beyond 
the convex lens Vviiere the refracted 
rays meet. This point depends upon 
the form of the lens, and the refracting 
power of the substance of which it is composed. The less convex 
or bulging the lens is, the more nearly it approaches a plane glass, 
and consequently the more distant is its focus. The more convex 
or bulging a lens is, the more obliquely will the raj^s, at any dis- 
tance from the centre, fall upon the surface, and the sooner, in 
consequence of their being more bent, will they meet the axis. 




* From the Latin /e??///, a bean, 
was first applied. This Las its tv> 



It was tlie donble convex, to vcliicli tlie name, lens, 
sides convex, like a bean. 



re^nciion of ghiss windoAvs. Defuiitinn of a Lms. Effects of a convex and concave 
I'?.; t pon li;jrlit. The sfilierc of a lens. Radius of a lens. Focus of a lens. Wha': 

1 2.; .!eis the focus more distant. 



CONVEX LENSES. 

Fig. 225. 



289 




Fiff. 226. 




I 




•c 



Thus a which is a sphere would converge the rays sooner than d, and 
the latter would converge them sooner than the less convex lens C. 

737. A concave lens disperses the 
rays. Thus let A and C be rays falling 
upon the concave lens D E instead of 
converging towards b in the axis of the 
lens, they will, by the first refraction, 
diverge to a and c, and by the second, 
to d and e. The perpendicular ray B 
b passes on in a straight line without 
any refraction. It will be seen at once 
that as the rays A C diverge on leaving 
f^' ^ * the glass, they will not, without another 

refraction, ever be brought to a focus. But a convex lens might 
collect these diverging rays. 

Concave lenses are used to receive converging pencils of rays, 
and to restore them to their original direction ; thus these differ- 
ent lenses in combination are applied to most important uses in the 
construction of optical instruments. 

Convex Lenses. 
738. Let A B be a convex glass, exposed to a very 
distant object E F, whose rays G A, G c, G B, fall 
on the glass, and passing through it, undergo a refrac- 
tion which will take place in such a manner, that the 
rays proceeding from the point G shall meet on the 
other side of the glass in the point g. The same thing 
will happen to the rays which proceed from every 
point of the object. By this alteration all the refract- 
ed rays A I,B m, C n, will pursue the same direction 
as if the object were at ef, and inverted ; and it will 
appear as many times smaller as the distance c^- shall 
be contained in the distance c G. We say, then, that 
such a glass represents the object E F behind it at ef; 
and this representation is called the image, which is 
=F consequently inverted, and is with the object itself, in 

Effect of a concave lens. How are convex and concave lenses used in coiniexion ? 
Explain fig. 227. 




290-.^- NATURyVL PHILOSOPHY. 

dKiK^ of the distances of the glass from the image, and of the glass 
from the object. 

It is clear, then, that if the sun v/ere the object, the image rep- 
resented at ef would be that of the sun ; though very small, it 
will be so brilliant as to dazzle tlie eye, for all the rays which 
pass through the glass meet in this image, and they exercise their 
double power of giving light and heat. Combustible substances 
placed in the focus of such a glass are instantly consumed. Met- 
als are melted, and even vitrified by it ; and other effects are pro- 
duced far beyond the reach of the m.ost active and intense fire. 

7.39. The reason for these effects is the same as in the case of 
burning mirrors. In both, the rays of the sun, diffused over the 
whole surface of the mirror or glass, are collected in the small 
space of the sun's image. The only difference is, that in mirrors 
the rays are collected by reflection, and in convex glasses by re- 
fraction. 

740. Whatever be the object exposed to such a glass, it always 
presents the image of it, which you see instead of the object itself. 
The following figure will render this more intelligible. 

Let A B C D be a convex glass, before which is 
placed an object, E G F. The rays which, from 
the point E, fall upon the glass, are contained in the 
space A E B ; and are all collected in the space A 
e B by refraction, so as to meet in the point e. In 
the sam.e manner, the rays from the point G, which 
fall on the glass, and which fill the space A G B, 
are comprehended by means of refraction in the space 
A ^ B, and meet in the point g. Finally the rays 
from the point F, which fall on the glass in the an- 
gle A F 15, are refracted so as to meet in the point 
f. Thus we shall have the image e gfm an in- 
verted position behind the glass; and it is as many 
times smaller as the distance D g is smaller than the 
, distance C G. 

In order to determine the place of the image egf, 
we must attend as v/ell to the form of the glass^ as to the distance 
of the object. As to the first, it may be remarked, that the more 
convex the glass is, or in other words, the more the thickness of the 
middle, C D, exceeds that of the extremities, the nearer the image 
will be to its surface. With regard to the distance, if you bring 
the object E F nearer to the glass, its image e f retires from it, 
and reciprocally. When the object, then, is very distant, the image 




Why would the sun's rays at c f fig. 227 be very intense 1 Kow does a convex lens 
differ irom burning mirroi'S .'' Err'aiu figure 228. 



AV 



VISION. 291 

falls in the very focus ; and the nearer you bring the object to 
the glass, the farther the image retires from it, and that in con- 
formity to a law in optics, by means of which you can always de- 
termine the place of the image for every distance of the object, 
provided you know the focus of the glass, that is the distance at 
which it collects the rays of the sun, in a space sufficiently small 
to set on lire a body exposed to it. 

741. The point where the rays meet is, as has been said, the 
place of the image. Now this point is easily found by experience. 
The diiFerent denominations of glasses are derived from it, as 
when we say, such agkiss has its focus at the distance of an inch, 
another at the distance of a foot, another at the distance of ten 
feet, and so on ; or more concisely, a glass of an inch, a foot, or 
ten feet focus. 
Fio''-_229. 742. Let A B C be a concave lens. If 5^ou expose to 
^ it at a great distance, the object E G F, the rays G A, 
/ G C, G B, proceeding from the point G, will undergo a 
B refraction, on leaving the glass, in the direction of A /, 
C 7?2, and B ??, as if "they had issued from the point g; 
and an eye placed behind the glass, at m, for example, 
will see the object just as if it were placed Sit egf, and 
f^^l in a sitiiation similar to that in which it is at the point 
G, but as many times smaller as the distance C G ex- 
ceeds the distance G g. Convex glasses, then, repre- 
sent the image of a very distant object behind them, 
concave glasses represent it before them; the former 
\i^<^r ^'^P^'ssent it inverted, and the latter in its real situa- 
"'' g"~ tion ; in both, the image is as many times smaller as 
the distance of the object from the glass exceeds that of the glass 
from the image. On this property of glasses is founded the con- 
struction of telescopes, spectacles, and microscopes.* 

Vision. 
743. Who can estimate the value of sight ! Without this sense, 

" Day, or the sweet appi'oach of ev'n or moi n. 
Or siolit of vernal bloom, or summer's rose. 
Or lloclcs, or herds, or human face divine," 

would ne'er to us return. And even though we might see the ob- 
jects immediately around us, and those above us in our own at- 

* The fig-nreto wliich this parao-ra|>li rof.N-s, with tlieiwo figures immediately prt ce- 
ding, and their explanations, ore I'rDin F-nlcr's "Letters." 



What is meant ]ry a glass of one incii or one foot focus ? Explain lig. 229. 



292 



NATURAL PHILOSOPHY. 



mosphere, but could not extend our vision beyond these liriiits, of 
what sublime enjoyments should we be deprived ! Confined as the 
soul is to a portion of matter which cannot soar beyond this ter- 
restrial ball, if all beyond its atmosphere v\^ere dark and unfathom- 
able, what a gloomy mystery would seem to hang over us ! But 
we are permitted to contemplate the system of worlds of which 
ours forms a portion, and the splendours of God's creation are re- 
vealed to our wondering gaze. We learn the motion, and laws 
which govern our own planet, by observing those of others. Our 
imaginations are awakened by the beauty and sublimity of the glo- 
rious firmament, and our hearts are warmed with love and admi- 
ration for Him wiio created this magnificent universe. How 



poetry, and devotion, indebted to 'the 



greatly then are science, 
power of distant vision. 

The Eye. 

744. The eye, by turns a microscope and telescope, is adapted 
to the purpose of viewing things near, or of extending its field of 
vision to far distant objects. On examining the structure of the 
eye, we find it a beautiful optical instrument, made in strict con- 
formity to the laws of science, and perfectly fitted to be acted upon 
by light, so as to form an image of the objects from which light is 
reflected. Was the Artist wiio formed this instrument ignorant of 
the effects to be produced? Or did the instrument itself blunder 
into existence, the offspring of a blind and fortuitous chance ? We 
may not pursue these speculations ; but cold must be the heart of 
that youth, who in studying these subjects, does not see something 
beyond the mere enunciation, and^ illustration of scientific truths, 
and whose devout affections are not animated as his understanding 
is enlightened ! 

745. The eye when viewed superficially, consists of the v\-hite, 
the iris and pupil, but by means of anatomical dissection various 
other parts^have been discovered. 

" The figure exhibits a front view of 
the eve, or the anterior portion of the 
eye ball. The white part surround- 
ing the centre is called the sclerotic^- 
" coat a a, and it is continued within the 
orbit, round the back part of the eye 
ball, being formed of a dense mem- 
brane, which includes, as in a bag, the 
other parts of the eye. It is perfectly 

* From the Greek, skleros. hard. 



Fi?. 230. 




Advantages of sight. The eye an optical instrument. 
exhibited in fig. 230. 



Mention the parts of the eye as 



THE EYE. , 



293 



opaque, and therefore is not continued over the front of the eye, 
but joins the transparent cornea^^ h h, which difl'ers from it chiefly 
in being completely pervious to light, and therefore serves like a 
window to admit it to the interior of the eye for the formation of ima- 
ges. Included within the cornea is the irisjf a sort of coloured 
fringe, usually either of a dark brown or of a grayish blue tint ; 
and hence the distinction between black, and blue or gray eyes. In 
the centre of the eye, surrounded by the iris, is a dark circular 
space of variable dimensions, called the pupil, through which the 
rays of light pass into the chambers of the eye. 

746. An horizontal section of the eye is represented here, in 
which the parts already described are shewn, as well as those of 
the interior. It will be perceived that the eye is enveloped in four 
membranes or tunics, the sclerotic coat AAA; the cornea B, 

connected with the former, in the 
front of the eye ; the choroid^ coat T 
T, which forms a lining to the scle- 
rotic coat, and on its opposite surface 
is covered by a black pigment, on 
which lies the interior coat of the eye, 
I called the retina^ R R, a delicate re- 
ticular membrane, expanded over the 
posterior chamber of the eye, and pro- 
ceeding from the optic nerve, O, by 
which sensations are conveyed to the 
brain. The interior of the eye, or the cavity surrounded by the 
coats just described, is filled by three substances called humours : 
The first, or the aqueous humour, D, is a fluid situated immediately 
behind the transparent cornea, and chiefly in the point of the iris. 
The second in situation is the crystalUne humour, C, directly be- 
hind the iris, being a solid, transparent lens, more convex behind 
than before ; and the third is called the vitreus humour, V, a kind 
of viscous solid mass, of a medium consistence compared with the 
other two, occupying the posterior chamber of the eye, supporting 
the other parts, and contributing chiefly to preserve the globular 
figure of the eye. Between C and D is the pupil or opening in 
the iris, I I, through which light is admitted into the eye ; and be- 
hind the iris the crystalline humour or lens is suspended in a trans- 
parent capsule, by the ciliary processes, L L, wliich proceed from 
the Iris."|| 

* From the Laliii coriietcs, bovney, or like a liorn. 

t So called because it has many colours like the rainbow or Tn'f!. 

t Fr.nn tiic Greek, Korion. § From the Catin, relc, a net. 

n MotFit's "Book of Science." London. 2d. Ed. p. 301. 




What docs the interior of the eye presiMit .'' Ilimiours of the eye, 

25* 



294: 



NATUAL PHILOSOPHY. 



Pig-. 232. 



447. We find that the eye has four coats 
or membranes, viz.; the sclerotic, the cor- 
nea, the choroid and the retma ; two humours, 
the aqueous, and viti-eous, and one lens, viz. ; 
the crystalhne. Let the figure represent a 
perspective view and horizontal section of the 
left eye. The eye-ball being nearly globu- 
lar, and about an inch in diameter, s s repre- 
sents the sclerotic coat, or white of the eye ; 
c c the cornea ; a a the aqueous humour ; i i 
the iris ; g the crystalline, lens ; V, the vi- 
ireus humour; r r the retina; and o o the 
ojitic nerve. 

748. " The eyes are situated in basin-shaped cavities in the 
skull, called the orbits, and there are various muscles attached to 
the ball of the eye, and to different parts of each orbit, which by 
their contraction give a certain degree of lateral rolling motion to 
the eye, and thus assist in directing the sight towards particular 
objects at pleasure. Eye-lids, also moved by muscles, and fring- 
ed by the eye-lashes, serve to guard the eyes from dust, and screen 
or shut them altogether from the access of too intense a light ; 
and there are glands for the secretion of fluid to moisten the cor- 
nea, and by the motion of the eyelids keep its surface clear, and in 
a state adapted to yield perfect vision."* 




LECTURE XXXVI. 

VISUAL ANGLE. FGRE-SHORTENING. PERSPECTIVE. INTENSITY OF 
LIGHT AND SHADE. CONVERGENCE OF THE OPTIC AXES. 

749. The great purposes of vision are to distinguish Ike magni. 
tude, figure, and distance of objects. The means of efTecting this 
are, 1. hy the visual angle, or the angle under which objects 
are seen; 2. the intensity of light, shade, and colours; 3. the 
divergence of the rays of light, and the convergence of the optic 
axes. 

* Moffat's "Book of Science." London. 2d. Ed. p. 394. 



Coats, humours and lens of the eye as seen at fig. 232. Situation of the eyes, use of 
muscles, eye-lids, &c. Objects of vision, and means by which they are perceived. 



VISUAL ANGLE. 



29.4 



I. The Visual Angle, 

750. The field of view is that open space around us in which 
objects are seen. But the eye has not the power of taking in at 
one view, the whole circle of the horizon. When a person stands 
with his face to the east, he cannot see the western horizon ; nor 
can he, at one view, behold both the north and the south ; because 
the range of human vision is less than half the circumference of 
the horizon. 

The scope of vision for the eye of man is not far from 45° or 
one eighth of a circle. Within this range the distant landscape, 
with its numerous objects may be depicted upon the retina of the 
eye. That is, a portion of the rays of light which diverge from 
objects in straight lines in all directions, falling upon the eye, are 
refracted by its transparent medium, and form a miniature picture 
upon the retina. 

751. Suppose a person surrounded by a globe of glass, divided in- 
to equal degrees, he would be able to say exactly what portion of his 
field of view was occupied or intercepted by any particular object, 

Fi^. 233. as the cross at c. He would then be 

able to form some judgment of its rela- 
t'>e size and situation. If the transpa- 
rent globe were smalKis seen by the sec- 
tion «, or large as at b, or c, the part of 
its surface apparently occupied hj any 
object beyond or within it, would bear 
the same proportion to the whole sur- 
face ; as the cross at a (i bears the same 
proportion to the small circle that hf 
and c g bear to the larger circles. 
Every circle being supposed to be divi^ 
ded into 360 degrees (which degrees are^ 
of course smaller in a small circle than 
in a larger one) the apparent magni- 
tudes of objects are judged of by observ- 
ing hov/ many of these degrees of the 
field of view each one occupies. And 
because the most convenient way of measuring a part of a circle 
of which the whole is not seen, is to measure the nngie formed at 
its centre by lines drawn from the extremities of that part; — as in 
the figure the angle at e being formed by the lines c e and g e the 




Field orvie\r. Extent ofthc field of view. Whatio represented at fig. '^SSi' \Vb.a' 
is meant by the visual angle ?- 



296 



NATURAL PHILOSOPHY. 



object c g is said to occupy a certain number of degrees of the 
circumference of the circle, or to subtend an angle of a certain 
number of degrees at its centre, which angle is called the visual 
angle. The objects at bf^nd a d subtend the same angle as the 
larger but more distant object at c g. But you will observe that 
the cross c g, which is about three times as large as a d, is also 
three times as far from the eye, and yet if no idea of their compara- 
tive distances entered into the computation of their magnitudes, 
the spectator, judging only from the visual angle, would suppose 
them to be of the same size. 

752. Let A B represent a tree with pencils of divergent rays issuing 
from the top and bottom. Entering the pupil of the eye, C, they 

Fiff. 234. 




are refracted by the crystalline lens, D, and form at the retina, a 
h, an inverted picture of the tree. The neai;er the tree is to the 
eye, the greater is the angle made by the meeting of the lines 
from its extreme parts. 

Pj^ 235. 1^2>. Again let A B represent a 

man viewed by an eye at C ; the ex- 
treme rays proceeding from this ob- 
ject form the angle A C B. The 
angle at C is the visual angle. If 
the same object be viewed at the 
point D, the visual angle A D B will 
B be greater. An object A B seen at 
C appears less than the same object seen at D where the visual 
angle is greater ; thus a tall man at a distance, may appear small- 
er than a child which is near. At four miles distance and without 
any interposing object, a man ceases to be visible. 

754. "Astronomers m^easure very accurately the angles under 
which we see the heavenly bodies ; and they have found that the 
visual angle of the sun is somewhat more than half a degree. If 
the sun were twice as far from us, this angle would be reduced to 
the half; and then it will not seem surprising that it should fur- 
nish us four times less light. And if the sun were 400 times fur- 




Tree seen at a distance. Man viewed at different distances. Visual an?ls of the 



VISION ASSISTED BY EXPERIENCE. 297 

ther off, his visual angle would become so many times less, and 
then that luminary would appear no greater than a star. We 
must therefore carefully distinguish the apparent magnitude of any 
object from its real magnitude. The first is always an angle 
greater or less, according as the object is nearer or more distant. 
Thus the apparent magnitude of the sun is an angle of about half 
a degree, whereas his real magnitude far surpasses that of the 
earth ; for the sun being a globe, his diametei- is estimated to be 
about TDOjOOO English mile;s, while the diameter of the earth is 
only 7912 English miles."* If you should ask a child or an igno- 
rant, unreflecting person, whether the moon is larger than a car- 
riage. wheel, he would probabiy answer you in the negative. A 
person better informed would tell you that the moon's distance 
when seen from the earth, greatly diminished its apparent size ; 
and he would explain this phenomena by shewing that the appa- 
rent magnitude of objects depended upon the greater or less de- 
gree of the visual angle. 

Vision requires the Aid of Experience. 

755. The real magnitude and distance of objects is not how- 
ever determined by vision alone. It is by comparison of things 
unknown with such as are familiar to us, that we are enabled to 
judge v/ith sufficient correctness on these points. Thus when ws 
see at a distance two persons walking, one of whom is an acquaint- 
ance, we judge of the height of the stranger by comparison- The 
visual angle assists us also to judge as to the distance of an object 
when its real magnitude is known. When the size of a distant 
object is known, its distance may be determined ; so on the other 
hand when the distance is known, the size may be ascertained with 
sufficient accuracy. 

756. Philosophers have been much in doubt with respect to the 
actual knowledge of external things gained by sight ; and v/hether 
we are indebted to this sense for our knowledge of the figure and 
magnitude of bodies. An instance is related by the celebrated 
optician, Chesselden, of his having, by means of a surgical opera- 
tion, given sight to a man who was born blind. f '• This person," 

* Eiiler. 

t The disease which occasioned llie blindness referred to is called a cataract (from 
the Greek, katarassf^, to confound or disturli.) It arises from the opacity of the crystal- 
line lens, which is thus rendered unfit for its purpose of refractinsj li^ht. By removing 
the lens out of the axis of vision, si^lit n;;ty be restored, if the retinn is not diseased. 
This operation is called cuudiing. In sonic cases ihe opatjue crystaUine lens is extract- 
ed. Glass lenses may be substituted for the lens of the eye for the pur[JOse of collecting' 
and refracting the rays of \\s.\\\. 

Apparent and real magnitude. Apparent magnitude considered leal. lieal magni- 
tude not determined by vision alone. Doubts of philosophers. 



298 NATURAL PHILOSOPHY. 

it is said " was at first dazzled ; he could distingiiish nothing as to 
the magnitude or distance of objects. All objects appeared so near 
that he wanted to handle them. And considerable time and long 
practice v/ere requisite to bring him to the real use of sight. He 
was under the necessity of serving a long apprenticeship, such as 
we perform during the term of childhood, and of which we after- 
wards preserve no recollection. This apprenticeship it is, which 
instructed us, that an object appears to us so much the more clear 
and distinct as it is nearer ; and reciprocall}^ that an object which 
appears clear and distinct is near; and when it appears obscure 
and indistinct, that it is at a distance. It is thus that painters, by 
weakening the tints of the objects which they wish to appear re- 
mote, and strengthening those which they would represent as nearer, 
are enabled to determine our judgment conformably to the effect 
which they mean to produce. And they succeed so perfectly, 
that we consider some of the objects represented in painting as 
more distant than others ; an illusion which could not take place 
if vision discovered to us the real distance, and magnitude of ob- 
jects."* 

Fore'Sliorlening. 

757. The appearance of objects to the eye depends much on their 
position. A globe always presents a circular image in" whatever 
manner it may be viewed ; but an egg may appear circular or 
oval, according to its position. A wheel when viewed in front,, ap- 
pears a perfect circle, when seen edgeways it appears like a broad 
straight band, and in other positions it appears oval. 

758. The knowledge of the actual figure of objects which we 
have gained by previous experience is suggested to us by seeing 
them, and we think of their true figure rather than of the outline 
presented to the eye. Whoever attempts to draw from nature 
finds a difficulty in delineating objects as they appear, in draw- 
ing a row of trees of equal size as they would appear to a person 
standing at one extremity, the nearest trees must be represented 
larger. If any long straiglU object, as a beam, be placed with 
one of its ends directly to the eye, that end only will be seen ; if 
the side be placed directly before the eye, the whole length will be 
seen ; in any intermediate position it will appear more or less 

* Eu'.er. 

Appearance of objects to a person who suddenly received sight. Learning to see. 
Method by which p:iiiiteis give the etFect of dist;ince. Apparent iigure of objects de- 
pends on position. Elfect of experience upon our judgment of things seen. DiHicuIty of 
drawing from nature. 



PERSPECTIVE. 



299 




shortened. The outhne on the retina being similar to the sliadovvr 
it would present on the wall in the direction of the person view- 
ing it. 

¥59. Painters terfn appearances v/hen the surfaces or lines are 
not placed so as to face the spectator, foreshortening. On look- 
ing abroad upon the extended surface, the distant portions are fore- 
shortened in proportion as they recede from the eye. Thus, sup» 
p.^. 23r pose a man standing on a plain at c, on 

g e ^ ' looking down he sees a portion of the 

' surface with very little fore-shortening ; 
an extent of five feet as a rf (that is al- 
. lowing five feet to be the height of the 
" '^ ^ '^ " eye) will subtend in the eye an angle 
of 45^5 viz. ; the angle a c d., or will appear 45^ long in his field o^ 
view, or halfof v/hat is subtended by the whole space from his feet 
to the horizon ; the next five feet will subtend a smaller angle, as 
dc f, and the next five feet a still smaller angle as/" eg; the angle 
g c b is smaller than the angley c g. Thus as, the man carries 
his view more and more forward, lines from the sitrface come to 
his eye more and more obliquely, until at last the light coming 
from the surface seems to be on a level with the eye. By under- 
standing the effect of this fore-shortening, we partly judge of the 
distance and nnagnitude of the objects situated at various points 
of view. , 



Perspective. 

769. The word perspective is from the Latin per, through, and 
specie, to look. The science of perspective teaches to draw on a 
plane surface true pictures of objects, as they appear to the eye 
from any distance in an oblique position. 

Fig. 237. "Suppose a straight view of siini- 

lar objects, as of the stone blocks 
or pillars represented here from a 
to S, to be viewed by a person stand- 
ing near C, then, because, as al- 
ready explained, objects appear 
smaller to the eye in exact propor- 
tion to their increased distance from 
it; the second block, if twice as far 
off as the first, would appear only 
half as large ; the third, if three times as far, would appear only 




Meaning fif the term foresliortcniiii^. l'"ti''i-t nf r.\tendiii<.^- tlic viow over a large sur- 
face. O'ljectortfiepciciicoofperipecnve. BuiUliiiis. trec?^, and pillaissco;! in porsiioclive. 



300 NATURAL PHILOSOPHY. 

one third as large, and so on to any extent, and for any other pro? 
portions; and if the 1,000th or any other nearer or more distant 
pillar subtended to the eye an angle less than the sixtieth of a 
degree of the field of view, it would be altogether invisible, even 
if nothing intervened between it and the eye. Then where the 
row ceased to be visible from the niinutenessof the parts, or from 
the fact of the nearer objects concealing the more remote, it might 
be said to have reached its vanishing point. 

761. Now it is very remarkable that in any such case of a 
straight line, or row of trees or pillars vanishing from sight, in 
whatever direction it points, east for instance, although the eye to 
see the near end of it would have to look about north-east, still the 
point in the heavens, or in a picture, or transparent plane before 
the eye, where the line would vanish, would be exactly east from 
the eye, and not in the slightest degree either to the north or to 
thd south of the east point, because the pillars happened to be north 
or south of the individual ; and therefore, if there were two or 
more rows of pillars parallel to the first, but considerably apart 
from each other, as the lines here, <2 S, ^ S, ^Z S, c S, and/" S, still all 
would vanish or seem to terminate in the very same point of the 
field of view. The reason of this is easily understood. Let us 
suppose a line drawn directly east from the eye or to the point S, 
viz., a line directly over the line h S, and that the line of pillars a 
S, also pointing east, is 20 feet north of the spectator, and the line 
h S, running in the same direction, is 20 feet south of him, then, 
evidently, for the same reason as the space between the top and 
bottom of the pillars, that is to say their height, becomes appa- 
rently less as their distance from the eye increases, so will the space 
between each pillar and the point corresponding to its place in the 
visual ray, or line along which the eye looks, become less, and 
the lines of pillars really 20 feet apart from the visual ray, will, at 
at a certain distance from the eye, viz., where 20 feet is apparently 
reduced to a point, appear to ]oin it, and the three lines will appear 
to meet in that point, beyond which they cannot be visible, and 
which is therefore called the vanishing point. 

762. "The conception of this truth may be facilitated by our 
supposing a star or phinet to be rising in the eastern point of tlie 
heavens, at the moment of observation ; then, if the three parallel 
lines were continued on to the planet, and were visible as far, they 
v\-ould arrive there with the 20 feet of interval between them just 
as they left the earth ; but as any planet, although many thousand 
miles in diameter, owing to its distance from the earth, appears 

Vanishing point. Explanation of the vanishing point in a picture. Suppose three 
parallel lines twenty feet apart to be continued to a planet or star. 



PERSPECTIVE. 



301 



only a point, much more would the space between any two lines 
only 20 feet apart be there undistinguishable by human sight. 
And what is true of a space of 20 feet between parallel lines, is 
equally true, as regards human vision, of a space of hundreds of 
thousands of miles; as a general rule, therefore, it holds, that all 
lines in reality parallel to each other in perspective, tend to and 
finish in the same vanishing point, viz., the situation of the line in 
which the eye looks when directed parallel to any one of those real 
lines. And this is true not only of lines of the same level or hori- 
zontal plane, viz., such as might be along the surface of the sea, 
but also of lines that are vertical or one above another, as those 
running along the tops and bottoms of the pillars, (see fig. 237.) 
or along the roofs and windows of the houses, and indeed of all 
lines in whatever situations, provided they are parallel to the visu- 
al ray. 

763. When it is ascertained, therefore, that aline in any natural 
or artificial object points 10 or 20 or any number of degrees north 
or south, or above or belov/, &c. ; the centre of the scene or pic- 
ture, that is to say, the poi?it of sight, or principal visual ray, then 
also is it known that all the parallels to that line have their vanish- 
ing point in that spot of the field of view, and a line supposed to 
be drawn from the eye to the heavens, or really drawn to the 
picture in that direction, marks the true vanishing point. 

784. it is explained now, why in a long arched tunnel, a bridge, 
or a cathedral with many longitudinal lines on its floor, walls, 
roof, &;c., all such lines seen by an eye looking along from one 
end, appear to converge to a point at the other, like the radii of a 
spider's web : and why in the representation of a common room, 
viewed from one end, all the lines of the corners, tops and bottoms 
f"'^- 238. of windows, floor, stripes on the 

carpet, corners of tables, &c., 
being parallel to each other. 




tend to the 



same vanishmg pomt 



as V, and are cut off by fore- 
shortening. 

765. By far the most import- 
ant vanishing point in com- 
mon scenes, is the middle of the 
horizon, called by painters, the 



horizontal line ; this in a picture, properly placed, is at the exact 



height of the eye. It is marked S in figure 237. and V, in figure 



General rule in perspective with regard to parallel lines. Metliod of ascerta'ning the 
vanishing point in a scene or pictnre. Why iines in a bridge, &c., wlien seen at one em^ 
leem to convcrL'"o ot the oilier. Iloriz'inta! line. 



26 



^2 NATURAL PHILOSOPHY. 

238. Because in houses, the roofs, foundations, floors, windows, 
&c., are all horizontal, the vanishing points of their lines must be 
somewhere in the horizon, and if the spectator be in the middle of 
a street or of a building, and be looking in the direction of its walls, 
their vanishing point will be in the centre of the scene or picture ; 
if he be elsewhere, it will beat one side. In holding up a picture 
frame, through which to view a scene suitable for a picture, it would 
be proper to raise it until the line cf the horizon appeared to cross 
at about one third from the bottom : — ^^this fact becomes the reason 
of the rule in painting, so to place the horizontal line. In be- 
ginning a picture, this Hne is usually the fxrst line drawn on the 
canvas, as marking the place of the vanishing points of all level 
lines and surfaces. And the eye of the spectator is supposed to 
be placed in the middle of it, and generally about as far from the 
picture as the picture itself is long, such being the extent of view 
which the eye at one time most conveniently commands. 

766. Dr. Arnott justly remarks, that " much of the delight which 
the art of painting is calculated to afford, is lost to the world, be- 
cause persons in general know not how to look at a picture. Un- 
less the spectator place himself where he can see the objects in 
true perspective, so that he may fancy himself looking at them 
through a window or opening, every thing must appear to him 
false and distorted. The eye should be opposite the point of sight 
of the picture, and therefore on a level with the horizontal line, 
and it should be al the required distance, which, generally, is as 
great, at least, as the length of the picture." 

II. Light and shade, or the effects of cclour and distinctness of 
outline upon the appearance of ohjects in a landscape or picture. 

76T. The apparent distance and magnitude of objects is affect- 
ed by distinctness of outline and brightness of colour ; or intensity 
of light and shade. 

Every one in the least familiar v/ith the effects produced on a 
picture by the use of colours, knows that distant views must be 
represented by faint shades, and with indistinct outlines. By 
deepening the shadows, or heightening the colours of a distant 
mountain, it seems at once brought nearer to the view, and the ef- 
fect of distance' is destroyed. Experience has thus taught us to 
associate the idea of distance with faintness of colouring. 

Light radiating from a centre becomes rapidly weaker as the 
distance from this centre increases. In looking upon a landscape 

Tlie first line ii?uall)' drawn on a picture. Manner in which a picture shouid be view- 
ed. Distant views, how represented. 



LIGHT AND SHADE. 2i}B 

illuminated by the sun, we see near objects, such as the flowers, 
fruit and fohage around us, distinct in outHne, and glowing with 
bright hues. Strong h'ghts and dark shadows prevail here. As 
the eye extends its range of vision, small objects are no longer 
visible ; there is a blending of colours and of figure until at last the 
outline of the distant mountain or ocean fades away into the blue 
sky. 

768. The painter, by the proper disposition of light and shade, 
and the management of colours, combined with perspective, is able 
to give a good representation of nature. Among the Chinese who 
are ignorant of perspective, pictures are figures of objects drawn 
on the same scale, and with a uniform vividness of colouring, 
whether the objects are supposed to be near or distant. With 
-them, the only way of representing distance, being to carry objects 
higher up the picture. This is as children and untaught persons 
usually attempt to, do in their paintings. 

769= The art of fore-shortening in drawing, and of reducing the 
size of objects as they are more distant, is called linear perspective. 
The varying of colour and the disposition of light and shade is 
called aerial perspective. The knowledge of the effect of light 
and shade in painting is called chiaro-oscuro.'* 

770. The effect of increased or diminished light in making ob- 
jects appear near or remote, must be obvious to any one who re- 
flects a moment upon the subject. When a fire breaks out in the 
night it appears to the spectator at a distance, as if it were very 
near ; and he often, for this reason, feels needlessly alarmed for the 
safety of his own dwelling. The bright red glare reflected from 
surrounding objects brings them nearer to his eye, and he sees the 
fire-men with their engines, and others running to and fro, in the 
bustle of the frightful scene as if almost before his own door. 
The seaman beholding distant mountains suddenly illumined by a 
bright sun, deems himself near to the land. Again the sun is ob- 
scured, and the coast seems to have receded from him. Objects 
appear larger when seen through a foggy or misty atmosphere. 
This is owing to the diminished intensity of light which makes them 
appear more distant without diminishing the visual angle subtend- 
ed by them ; for to the man at forty rods distance who subtends 
the same angle as the one at twenty rods distance, the same object 
must appear twice as large. 

* Italian words signifying clear and obscure. 

Defect in Chinese Pictin-es. Linear perspective. Examples of the cllect of increased 
or diminished light. A fire seen in the night. Distant mountains illuminated by a bright 
sun. Effectsofa foggy atmospheic. 



304 NATURAL PHILOSOPHY. 

Thus, in the dim twilight, objects seem magnified ; and the su- 
perstitious, heightening this illusion by terror, readily convert a 
guide-board into a ghost ; — passing a church-yard in the night 
when the atmosphere is charged with vapours, fear may readily 
combine with the optical deception produced by such an atmos- 
phere, and cause the white monum.ents to appear as colossal spec- 
tres, and the sapling willow with its pensile branches waving in 
the breeze, to seem like a huge giant tossing its arms to and fi'o. 
Many a ghost-story has arisen from appearances, which the igno- 
rant, not understanding, have deemed supernatural. Strange lights 
which, as they supposed, warned them of some coming event, 
might, by a knowledge of the laws of optical reflection, have been 
traced to their origin, perhaps a candle at a neighbouring window 
or in the range of a mirror, which itself unseen, may reflect light 
upon a wall. 

771, The inhabitants of the Hartz mountains in Germany, had 
many legends of the Spectre of the Brocken.^ This was a gigan- 
tic figure which had often been seen walking on a certain ridge of 
the mountain just at sunrise. A philosopher who had learned that 
the wonders of magic may often be referred to the operations of 
nature, went with a friend to the opposite ridge to watch this phe- 
nomenon. Many mornings passed and the spectre had not made 
his appearance. At length, as the horizontal rays of the sun fell 
in a dense fog which hovered over the valley beyond, the spectre 
of the Brocken was seen. But he was now in company with another 
spectre of equally gigantic dimensions ; and the two very uncivilly 
mimicked every motion and attitude of the philosopher and his 
friend ; when they ran the spectres ran, and when they stood still 
the spectres were motionless. The philosopher explained it by 
saying that these figures were merely sliadoivs of himself and 
friend, /or me^ by their interce'pting the rays of the rising sun which 
illumined the misty aimosj^here on the opposite ridge of the moun- 
tain. The apparent m.onstrous size of the figures was ovWng to an 

* The Brocken is theloftiest of the range of mountains lying in Hanover, (Germany,) 
and celebrated for its picturesque scenery and geological treasures. "Fiomtheeur- 
liest periods," says Brewster, "the Brocken has been the seat of the marvellous. On its 
summits are still seen huge blocks of granite, calk d the Sorcerer's chair and the Altar. A 
spring of pure water is known by the name of the iNIagic fountain, and the Anemone of the 
Brocken is distinguished by the title of the Sorcerer's Hower." 

The Saxons are said to have worshipped their sanguinary idols upon the summit of this 
mountain, even when the plains below were enlightened by Christianity. We can scarce- 
ly wander that with all these associations with the Brocken, the gigantic spectre should 
have been an object of terror to the ignorant and superstitious inhabitants of that wild 
region. 

Oftwilio'ht. Optical illusions. Spectre of the Brocken. 



CONVERGENCE OP THE AXES OP THE EYES. 305 
Fig. 239. 




optical illusion arising from the faintness of the sha^ 
had the effect of making them appear distant. 



which 




III. Divergence of the Rays of Light ; and Convergence of the 
Optic Axes. 

112. Divergence of the rays of light assists in enabling us to 

judge of the distance or magnitude of objects. Suppose E F to 

Fig. 3-^0. be the pupil of the eye, 

E_ and light entering it 

from an object at a. 
The rays spread with 
a large angle, or are 
more divergent than 
■^ those from an object a b. 

At c and d they open at still smaller angles, or are less divergent. 
Now the eye to form an image on the retina, must make an effort 
to bend or refract the rays exactly in proportion as they are di- 
vergent when they fall upon the crystalline lens, and the degree of 
effort thus made becomes a kind of measure of the distance and 
magnitude of the object. Painting cannot give this effect, for while 
in nature every object according to its distance is sending rays 
which meet the eye with different degrees of divergence, the rays 
from a picture from a single plane surface, have, in every part, the 
same divergence. The eye does not need to exercise the same 
effort of refracting the rays in accommodation to different distan- 
ces ; and this, in some measure destroys the illusion that painting 
might otherwise cause. 

773. By the convergence of the optic axes, we mean that the 
axis of each eye is directed towards one point, or that the two ax-es 

Effect of divergence of light in enabling us to judge of distance. Painting cannot giva 
this effect. Convergence of the optic axes. 

26* 



306 



NATURAL PHILOSOPHY 



converge when both eyes are looking towards the same point. 
The optic axis is the axis of the crystalh'ne lens continued to the 
object at which we look. This imaginary axis back of the crys- 
talline lens terminates at the middle of the retina, and this point is 
called ihe point of distinct vision. The inclination or convergence 
of the optic axes is greater for near objects than for distant ones. 
Thus suppose E and F (fig. 240.) to mark the places of the two 
eyes ; if directed towards an object at a, it is evident that the two 
optical axes must have a greater convergence than if the eyes 
were directed towards h. When we lock at very distant objects 
the axes of the eyes seem parallel, and we cease to judge of dis- 
tance by their convergence. 



LECTURE XXXVII. 

DURATION OF IMPRESSIONS UPON THE EYE. SINGLE VISION. IM- 
PERFECTION OF VISION. OPTICAL INSTRUMENTS. SHADOW. 



Duration of the Impression of Light upon the Eye. 

174. When a stick burning at one end is whirled by the hand^ 
a circle of light is seen, marking its path. As the burning end of 
the stick can only be in one point of the path at the same instant, 
it is manifest that the impression of its light continues on the eye 
after the object has left particular points from whence it was seen. 
It has been found that the light of a live coal, placed at the dis- 
Fisr. 241. tance of 165 feet, continued its impres- 

sion on the eye during the seventh part 
of a second. A toy called the thau- 
Tjiatrope^^hQ,^ been invented to illustrate 
this phenomenon. The figure is a cir- 
cular card with two strings fixed to it. 
On one side of the card there is drawn 
any object, as a carriage, and on the 
other a man in the attitude of driving. 
When the card by means of the strings, 
is twirled round with 




some degree of 



* From two Greek Avordssigrni 



"ying to learn icovders. 



In what case greatest. Examples to prove that the impression of light upon the eye 
remains after the object which produced it is removed. 



SINGLE VISION WITH TWO EYES. 307 

velocity, the carriage and the driver appear as one picture. Now 
as one side must be out of sight while the other is towards us, it 
follows, that we see at once what is drawn upon both sides of the 
card, in consequence of the duration of the impression of light on 
the retina, when the object from which it proceeds is removed. 

Cause of Single Vision with Two Eyes. 

775. It is in consequence of the power of directing the axes of 
both eyes in one direction, or of their convergence, that, though 
an image is formed on each retina, the mind sees but a single ob- 
ject. This singleness of vision would take place if, nistead of two, 
we had a much greater number of eyes, that is, supposing they could 
all direct their axes to the same point. By pressing one eye aside 
when we are looking at any object, the axis is turned away from 
its line of inclination towards the axis of the other eye, and we see 
a double image. Images formed at the same time, of an object 
nearer to, or farther from, the eye than the point where the axes 
meet, must appear double, because they are not formed at the 

Fig. 242. point of distinct vision. Supposing 

this point to be a a in the centre of 
the retina, and that the axes are di- 
rected towards the object at b, the 
50^^^^-" image is seen single. But without 

changing the direction of the axes attempt to look at an object be. 
yond b as at c, and tFie image on each eye will be formed outside 
the point of distinct vision, and v/ill be seen double. On the con- 
trary, attempt to look at an object at o while the axes are directed 
towards h, and the image will be formed inside of the point of sight, 
and appear double. A simple experiment will illustrate this. 
Flold the two fore fingers in a line from the eyes, so that one may 
be a little more distant than the other, by looking at the more dis- 
tant the nearer will appear double, and by looking at the nearer 
the more distant will appear double. 

776. When the crystalhne lens has ceased to be homogeneous, 
either from disease or age, small images, such as the letters of a 
book, will be seen double. Double vision is sometimes apparent 
in persons who are dying ; it is also often ocgasioned by madness 
or intoxication. Many animals never see objects with more than 
one eye at a time, as some birds, lizards, and fishes. Some spe- 
cies offish can only see such objects as are situated above them. 



In what case should we sec double. Point of disliact vision. DiUl'rout causes of 
double vision. 




308 



NATURAL PHILOSOPHY. 



Imperfection of Vision. 

777. When both eyes do not seem to be directed to the object 
at which a person is loolving, he is said to be squint-eyed, 
Short-sightedness arises from a too great convexity ofthe crystaUine 
lens. In such case the rays of light are converged so much that 
they are brought to a focus, before reaching the retina. Let I> 
represent the crystalline lens, with pencils of light from A B falling 

Fig. 243. 




upon it. They are collected into a focus at F, from this point the 
rays proceed in a diverging manner, and form at the retina a &, a 
confused image. By bringing the object viewed near to the eye^ 
as is done by short-sighted persons, the rays fall upon the eye 
more diverging, and are not so soon converged by the crystalline 
lens, so that the focus will fall upon the retina ; for the nearer an 
object is brought to a lens, the farther the image recedes from it. 

Short-sighted people are assisted by concave lenses. The ef- 
fect of such lenses is to diverge rays of light. Thus the glass A 
Fig. 244. B causes the rays which 

^??==^ A ^^ fall from the object O, to 

^ /L— - Wy ) \ ■ -— =_^5 become more divergent ; 

\r~~'^~Wy — I ^Ja^ and the crystaUine lens C 

^'==^ B D, which is too convex, 

then converges the rays, and the image or focus is thus thrown as 
far back as the retina R. Without the aid of concave eye-glass- 
es, near-sighted people cannot see objects at a little distance with 
any distinctness. As age advances the eye becomes flatter, and 
consequently elderly people, who are near-sighted in youth, often 
see without the aid of glasses of any kind. 

778. There is another defect of vision called long-sightedness. 
This arises from a want of sufficient convexity in the crystalline 
lens. After middle age, and sometimes earlier, the eye becomes 
flattened in consequence of the decay and shrinking of the refract- 



Squinting. Short-sightedness. Why do the short-sighted biing objects very near to 
the eye ? EiFeet of concave lenses in assisting vision. Cause of long-sightedness. 




OPTICAL INSTRUMENTS, 309 

iiig humours. This change is denoted by a tendency to hold a 
book at a greater distance when reading. This is because the 
rays of hght are not converged by the flattened crystalline lens, 
sufficiently to bring them to a focus on the retina, but this focus, 
or the image of the object would be formed at a point beyond. 
But a convex lens interposed between the object and the eye, by 
bending the rays to a greater convergence, brings the focus for- 
v/ard, and the image will be formed on the retina. Thus the spec- 
tacles worn by aged persons are usually convex lenses. They 
do for the eye that portion of the labour of bending the rays of 
light, which it has not the ability to perform for itself. The func- 
tions of the eye being thus aided, the benefits of sight in aged per- 
Fig. 245. sons are secured. Let C 

D represent the crystalline 
lens, and A B a convex 
glass or spectacle lens, 
then the object o, at about 
six inches from the eye will form a perfect picture of the object at 
R, the retina. But if the lens A B be removed, the image at that 
distance will be confused, and, it will be necessary to withdraw 
the eye to three or perhaps four times the distance, and if it be a 
minute object, the unassisted eye may not be able to distinguish it 
at any distance. 

779. The cataract is a disease occasioned by the crystalline lens 
losing its transparency. This opacit}^, if total, prevents the pas- 
sage of rays to the retina ; if partial, it renders the image there 
formed, very dim and indistinct. The operation, or couching, as 
it is called, for the cataract, consists in taking the defective lens or 
humour from the eye, in which case light can again revisit the 
"dim orb." But the principal converging power being gone, the 
image, instead of being formed on the retina, will be at a point be- 
yond it. A convex artificial lens here answers the purpose of the 
natural one. Thus persons who have undergone the operation for 
the cataract, usually wear very convex spectacles. 

Optical Instruments. 

780. The ancients appear to have been better acquainted with 
mirrors, or glasses for the reflection of light, than with lenses or 
glasses for its refraction. The burning mirrors of Archimedes 
are named in history as far back as two hundred years before 
the Christian era. 

Indication of this defect. Elfectof a convex lens wliere the eye is too Hat. Catai'dCt 
and its remed3^ Optical glasses used by the aucienls. 



§10 NATURAL PHILOSOPHY. 



Spectacles. 

781. Spectacles are lenses mounted upon a metallic frame, so that 
they can be conveniently worn before the eyes. It is unnecessary 
to repeat what we have said on the use of convex, and concave 
glasses. The spectacles worn by aged people, as above remark- 
ed, are convex lenses. They assist the flattened cr3^stalline lens of 
the eye to converge the rays of light. The common eye-glasses 
carried by near-sighted people, are concave lenses which counter- 
act by their divergence, the effect of too much roundness of the 
refracting lens of the eye. It is not ascertained by whom specta- 
cles were invented. They were not in use before the thirteenth 
century, though the magnifying power of convex lenses was un= 
derstood at an eailier period. 

Microscopes. 

782. The microscope* is designed to assist the eye in viewing 
minute objects. 

A double convex lens, or a small globe of glass, is the simplest 
kind of microscope. When applied to small objects, as the sta- 
mens or pericarp of a plant, the surface of a crystal, or the letters 
of a book, it exhibits parts not visible to the naked eye, or magni- 
fies such as are visible. Without the aid of the microscope, we 
cannot view objects distinctly, if held nearer to the eye than three 
or four inches. For when an object is brought nearer and nearer 
to the eye, we at length reach a point within which sight becomes 
confused. This point is called the limit of distinct vision, and varies 
a little in different persons. The cause of this confusion of sight 
is, that the divergence of the rays of light from a near object, is 
too great for the refracting power of the crystalhne lens of the eye 
to collect them, so that an image may be formed on the retina. 

Thus if an object be placed within an inch or two of the eye, the 
rays which proceed from it are too divergent to be refracted so as 
to form a focus on the retina. But let the same object be viewed 
at the same distance from the eye by the assistance of the convex 

* From the Greek micros, minute, and scopio, to see. 

Spectacles. Eye-glasses. Use of the microscope. Simplest kind of microscope. 
How does the microscope enable us to see objects nearer to the eje, than when the vigion 
is unassisted? 



SINGLE MICROSCOPE. 



31t 




•-.r 



lens B, whose focal distance is B A> 
those rays diverging from the object 
which fall on the surface of the lens, 
will be refracted at its two surfacesj 
and emerge from it nearly parallel to 
each other, consequently the object 
is capable of being viewed by the 
eye on the side B, under a greater 
angle than it could be seen without 
the lens. 

783. And, because the object is seen under a greater angle, it 
is magnified ; and minute portions, which were before invisible 
because they did not occupy sufficient space on the retina, are now 
brought into view. Even by looking through a pin hole in a 
piece of coloured paper, the letters of a book will appear larger, 
and more distinct, than when seen in the ordinary way. This 
greater distinctness is owing to the exclusion of the diverging rays 
of each pencil of light, which, falling obliquely upon the eye, are 
not brought exactly to the focus with the central rays, and there- 
fore tend to confuse an image. The smallness of the pin hole al- 
lows only the axes of the several rays to pass, and these proceed 
in lines almost parallel. Through such an aperture letters ap- 
pear very large and distinct when a book is held within an inch 
of the eye. On removing the perforated paper, and attempting 
to look at the letters at the same distance as before, there is no dis- 
tinct vision. 

784. The single microscojje consists of a convex glass, called ti 
.magnifying glass, in the focus of which is the object. By means 
of the converging power of the magnifier the eye may be brought 

Fig. 247. very near the object. The 

rays from the object at O being 
bent at A B, proceed nearly 
parallel to the pupil C, and faH 
on the crystalline lens D in 
such a manner as when again 
refracted they form a magnifi- 
ed image on the retina R Rs 
The more convex a lens is the 

shorter is its focus, and the shorter the focus of a lens, the greater 

is its magnifying power. 

785. It is important for many purposes to know the exact mag- 
nifying power of a microscope ; that is whether it makes an object 




Why does the inicroscopn itinvnir\' 
book through a pin hole nridc in [j;'.[).'i 



ij.ct,^'? i''ri';(i of looki.ig I1J10I1 the letlci-s of a 



312 



NATURAL PHILOSOPHY. 



appear ten, fifty, or a hundred times larger than when "viewed by 
the naked eye. 

This magnifj'ing power depends on tlie difference of the distance 
of the object from a lens, and the distance when seen without its 
assistance, or in other words on the ratio between the focal distance 
of the lens and the limits of distinct vision. This latter point va- 
ries in different persons, and at different periods of life in the same 
person. In reading, the most common distance at which we hold 
a book fi'om the eyes, is, probably, about ten inches. When we 
examine the different parts of a flower or an insect we hold it 
nearer. The focus of the eye has been called ten inches, by some 
writers, because this number, being a decimal, forms an easy mul- 
tiplier or divider in optical calculations. Thus a lens which re- 
quires for distinct vision, the object to be one inch from it, — that is, 
from the centre of the lens, — vre must divide 10 the limit of distinct 
vision, — by 1, which will give 10, therefore such a lens will in- 
crease the apparent size of an object ten tim.es. 

786. An inch lens then is said to have a magnifying power of 
ten; but this only denotes the increase of the length and breadth 
of an object. Such a lens has in fact a magnifying power of one 

"' "'" hundred; that is, the magnified image 

would, in its superficies, occupy one 
hundred spaces when the real object 
would occupy but one. Thus suppose 
the square a the real object, and A B 
its magnified image. By counting the 
squares it v/ill be found that the image 
is ten times longer and broader than the 
object, but there are one hundred 

squares as large as a, therefore A B is in reality one hundred times 

larger than a, 

787. The compound microscope consists of Uvo or more convex 
lenses, one of which, called the ohjeci-glass, is used to form an 
enlarged image of the object, and the other, called the eye-glass, 
magn'ines the imac^e. In the si!\gle microscope, the magnified 





J 


b'lg. 24 


«. 






1 1 1 










1 




















1 








1 1 




1 j 


1 














i 














i 














1 


































[ 




1 


-» 



"object is seen ; in th 
but its mag 



nified image. 



compound microscope, the object is notseenj 



On what the magnifyina; power of a microscope depends. Focus of the eye, or point 
-.of distinct vision. Why is an inch lens said to have a magnifying power often ? TLc 
real magnifying power of en inch lens. Perls of the compound m:cro^co[ie. 



SOLAR MICROSCOPE, 



313 



Suppose an object a h, to be placed a tittle be- 
yond the focus of the object-glass c d, the rays 
of light proceeding from it will be collected on 
the other side of the lens and form an enlarged 
and inverted image at g h. The eye-glass ef, 
again magnifies the image which is formed on 
the retina at A B, in an upright position. 

788. The Solar microscope is so named be- 
cause the object is illuminated by the solar light 
reflected from a plane mirror. Two lenses are 
also used ; they are contained within a tube, 
which, when the microscope is used, is placed in 
a hole in the window-shutter of a darkened room. 
The reflector is outside the shutter, in order that 
it may receive the solar rays ; these fall upon a 
large convex lens called a condenser, whose of- 
fice is to collect the rays and throw them upon 
an object placed within its focus. These rays 
are again refracted and form behind the second lens a magnified 
image of the object which is thrown upon a screen. Let P Q, 
represent the reflector of a solar microscopcj S incident rays, 

Fig, 250. 



X . / / / / /J" 





4^ 


^k 


I n ^ 


-i>4l 


i / ^yy 


B^ 




'^<^ 




\^^ I 


^ 



--F 



•which being reflected upon the condenser, or the lens X Y are con- 
verged and brought to a focus at A B. Now the object, being at 
this focus, reflects this concentrated light from its surface in all di- 
rections, the rays which fall upon the lens C D, are refracted and 
form the magnified image E F, upon a screen or the wall of an 
apartment. 

789. The solar microscope has opened a new field of wonders. 
The common microscope had previously done much towards re- 
vealing the fact, that man lives in a world of which he knows 
comparatively little. The young student in natural history, who. 



Explain tlie manner in which objects are viewed through a cotni)ourid microscope. 
Solrr microscope. Explain the manner in which the solar ni'croscope is used. 

27 



314 



NATURAL PHILOSOPHY. 



for the first time, examines an insect through a microscope, is as- 
tonished at the transformation of a fly into a huge monster, with 
eyes of fire, and a proboscis like an elephant, or at seeing in a 
piece of wood, regular hexagonal divisions as large as the cells in 
a honey-comb. But the solar microscope has shewn the exist- 
ence of life where it had not before been suspected. The fine dust 
upon a fig, or the rind of a cheese, when examined through this 
instrument, is seen animated with creatures scrambling about like 
pigs among rocks, and a drop of vinegar appears an ocean filled 
with sea-monsters. Of all the wonders exhibited by means of the 
solar microscope, the process which takes place in the crystalliza- 
tion of salts is, perhaps, the most striking ; where particles of mat- 
ter not gifted with intelligence or even life, are seen taking their 
respective places, to form a cube or prism, with as much precision 
as a company of soldiers form themselves into a phalanx or 
platoon. 

Magic Lantern, 

790. In this instrument the light of a lamp is substituted for solar 
light. The objects to be represented are painted on plates of 
glass of a size to be conveniently passed through a narrow open- 
ing in a tube between two lenses. The tube is fixed in the lan- 

Fi^. 251. tern. The experiment is per- 

formed in a dark room. A rep- 
resents the magnifying lens, B 
the object introduced through an 
opening in the tube, C the con- 
densing lens, D the argand lamp, 
E the concave reflector which 
collects and throws forward upon 
the condensing lens, the rays 
which would otherwise be partially lost. F is the image formed on 
a screen or white wall. 

The farther the lantern is withdrawn from the screen the great- 
er the image will appear, though it maybe indistinct by being too 
far removed. In order that the image may be seen erect, the ob- 
ject must be inverted. 

Camera Ohscura. 

791. The eye is a camera obscura ;* that is, light from with- 
out, enters a dark chamber by means of a small aperture, the pu- 

* Literally, a dark diamher. 




Discoveries made by means of the solar microscope. Construction of the magic lantern- 



CAMERA OBSCURA, 



315 



pil of the eye, and being refracted by the convex crystalline lens, 
forms an image on a screen behind it, viz., the retina. Let a dark 
room represent the eye, an aperture in a window-shutter the pu- 
pil, and a convex glass lens the crystalline humour ; rays of light 
from without, entering in at the aperture and refracted by the lens, 
fall upon a screen or the wall of tlie apartment and form an 
image of the objects without, from which the rays proceeded. Jf 
the chamber had a soul, and a communication by some contri- 
vance like that of the optic nerve, could convey the image to it, 
then the chamber, or rather the soul within it, could see. But 
the image on the screen is inverted ; — and does the soul within 
the chamber see things upside down ? Some philosophers have 
asserted that this is the case, and that experience teaches the 
child to regard objects in their true position. But let us in the 

first place consider that the soul 
has no material eyes, and, there- 
fore, that there can be no analo- 
gy between mental and bodily 
vision; and secondly, if the soul 
were hehind the screen, and 
looking down upon the inverted 
picture (like the man in the fig- 
ure) the objects there delineated 
would appear in their true position. 

792. LetC D represent a darkened chamber, or large box with 
an aperture at L, where is fixed a convex lens of such a curva- 
ture that the focus of parallel rays falls upon the opposite wall. 
The object A B being at a suitable distance an inverted imafje 




Fisr. 253. 



will be formed on a screen or 
on the opposite wall ; for the 
pencil of light which proceeds 
from A will converge to a, and 
the pencil from B will con- 
verge to C, and the intermedi- 
ate points of the object will be 
reflected between a and C. 
B The picture is viewed from an 
A plane mirror may be so placed 
as to reflect upon the lens the object to be delineated ; in this the 
camera obscura bears an analogy to the solar microscope. When 
artificial light is used, as of a lamp, we have then the magic lan- 
tern. The eye is properly likened to a camera obscura ; the 




opening in the top of the box. 



Resemblance between llie camera (fccura and t!ie eye. Arc objects; in reality soon by 
the eye in an inverted position '.' Construclion ufa camera obscura. 



316 NATURAL PHlLOSOPfiY. 

pupil being the aperture in the chamber, the crystalline lens the 
convex glass which is placed just behind this aperture, and the 
retina the screen or wall on which an inverted image of the object 
is depicted. 

Telescope. 

793. The microscope and telescope* are used for very different 
purposes, the one to examine minute objects placed very near lo 
the eye, and the other to view large and distant objects. The 
telescope does indeed make use of the microscope in its operations, 
or rather an image is first formed of a distant object by means of 
a convex lens or a concave mirror, and then viewed and magnified 
with a microscope. A refracting telescope has the image formed 
by means of a convex lens. A reflecting telescope has the image 
formed by means of a concave mirror. 

794. The astronomical telescope is the most simple ; it consists of 
two convex lenses, an object glass, and an eye glass. 

The object glass is directed towards the object. The eye glass 
is at that end of the instrument at which the eye is applied. 

Fig. 254. S^PP«^^ ^ ? ^° 

Q represent rays irom 

"^^^TT"--— --«..,.______^ Q, some distant object, 

I ' ^II:^ ■ ^^CTT""^ TT^^ as a star, then the im- 

13 U^ ' ' J ^ — — ii-^^ age formed by the ob. 

'=^-'^ hji^^<^ ^ ject glass C being 

viewed through'^the eye glass G H, will be magnified according to 
the magnifying ^flliik- of the lens G H. Thus if the object glass 
have a magnifying power equal to 10, and that of the eye glass 
be equal to 6, the object will be magnified 60 times, or 10 X 6. 
The image will be inverted, but this is not an important defect, 
because the use of this telescope is confined to observations of ce- 
lestial bodies. 

795. Terrestrial telescopes, used for ship and spy glasses, have 
two additional lenses in order to obtain erect views of the object. 

Thus A B, the object glass, forms an inverted image n m of the 
object M M. In the astronomical telescope this image would be 
viewed at L. But the pencil of parallel rays here crossing each 
other falls upon the lens E F, (which is of the same focal length as 
CD;) this lens collects the rays into a focus where the erect im- 

* From two Greek Avords, the meaning of which is io see at a distance. 

■ Difference between the microscope and telescope. Astronomical telescope. Terres- 
trial telescopes. 



TERRESTRIAL TELESCOPE. 



317 




age m n appears. This image is viewed by the eye at E by 
means of the eye glass G H. The additional lenses do not mag- 
nify, for their focal length is the same as that of the first eye glass. 
Were they smaller, or more convex for the purpose of magnify- 
ing, the light would be injured and the field of view limited. 
• 796. The reflecting telescope has two concave metallic mirrors, 
with two plano-convex eye glasses. 

797. The telescope magnifies as many times as it presents ob- 
jects under an angle greater than is presented to the naked eye. 
The moon, for example, appears to the naked eye under an angle 
of half a degree; consequently a telescope magnifies 100 times 
when it represents the moon under an angle of fifty degrees. If it 
magnifies 180 times, it would represent the moon under an angle of 
90 degrees, in which case the moon would appear to fill one q-uarter 
of the heavens. Euler, a celebrated German philosopher wished, 
as the thing of all others most desirable, that he had a telescope 
which would magnify 100,000 times, so that he could then see the 
moon as if only half a mile distant, and observe the inhabitants 
and animals which may be upon it. But the little boy might with 
equal propriety wish his rocking horse were alive, and the little 
girl that her doll would talk, as philosophers amuse themselves 
with wishes that can never be accomplished. There are limits 
to human efforts ; and it is not probable that men will ever build 
a tower high enough to reach the heavens, or construct a teles- 
cjope which will make us very near neighbours to any of the ce- 
lestial orbs. 

798. The great telescope of Sir William Flerschell, was four 
years in building ; it was forty feet in length, the great mirror was 
four feet in diameter, and it magnified 6000 times. Its focal 
length was forty feet. The star Sirius, when viewed through this 
telescope, appeared of the size and brilliancy of the sun. A sixth 
satellite of Saturn was discovered the day on which the telescope 
was completed. Improvements in optical instruments have ren- 
dered an apparatus so very cumbrous, the less necessary by com- 
bining in a smaller compass greater advantages than were possess- 
ed by this. 



Reflecting telescope, 
telescope. 



Cause of the magnifying power of the telescope. 

27* 



JlerschcU'- 



318 



NATURAL PHILOSOPHY. 




Shadow. 

799. For the formation of a shadow two things are necessary ; 
1. a luminous, and 2. an opaque body. The opaque body inter- 
rupts the passage of the rays from the luminous body and causes 
darkness beyond it, and this produces upon the wall or a screen, 
what is called a shadow, it being a dark image of , the opaque ob- 
ject. Darkness, you will recollect, is but a negative ; it is merely 
the absence of light, as cold, of itself, has no actual existence, but 
simply denotes the absence of heat. 

Fjg, 256. 800. There are three 

things to be observed 

with respect to the form 

and size of shadows ; 1 . 

Where the luminous body 

is smaller than the opaque 

^iody ; let L be a lumi- 

nous body, smaller than 

L the opaque body O. It 

is evident from the diverging of the rays, that the shadow will be 

larger in proportion to its distance from the object. 

Pj^^ 257. 2. JVhen the luminous body 

is larger than the opaque body ; 
kiL Thus let A be a luminous body, 
\^ (the sun,) and B an opposite bo- 
^^ dy, (the earth,) the shadow will 
_r.|'l^ be in the form of a cone, and 
gradually diminish in size till it terminates in a point. 

3. When the luminous body is 
of the same magnitude as the 
opaque body. Here the shadow 
will be that of a cylinder. Thus 
let A be a luminous body of the 
same magnitude as B. The lines a m and a n are parallel, and 
if the shadow of B v/ere extended to infinity, it would be cylin- 
drical. 

801. The darkness of a shadow is In proportion to the intensity 
of light. Though as surrounding objects reflect light, the shadow 
itself will be in some measure illuminated. Were it not for this, 
shadows would appear perfectly black. 

A number of lights will cause as many shadows of the same ob- 





Cause of shadow. Cause of the difference in the form and size of shadows. Cause 
cf the different degrees of darkness in shadows. 



NATURE OP LIGHT. 



319 



Fisf. 259. 



; that is, in case the lights are not situated in the same line of 



direction. Suppose a ball A, to re- 
ceive light from three lamps, B C and 
D, the light B will produce the shadow 
1), and the light C will produce the 




the 

two 



shadow c, and the light D the shadow 
d, but the shadows will not be very- 
dark, because they are receiving some 
light from the two lamps which are 
out of their line of direction. The ball 
hides the hght from the lamp C ; but 

wall at the place of the shadow c is illum.inated by the other 

lamps. 



LECTURE XXXVIIL 



NATURE OF LIGHT. DECOMPOSITION OF LIGHT. DISPERSION OF 
Jl,^ LIGHT. RAIN-BOW. ABSORPTION OF LIGHT. 

802. The light which proceeds from the sun, and which appears 
white, is reflected in a variety of colours from the foliage of trees, 
the petals of flowers, and other innumerable objects around us. 
How beautiful, how kind, and how wise is this arrangement. A 
clear transparent light meets our gaze when we look upwards or 
around us in space ; but when we look down upon the earth, our 
eyes are feasted by the brilliant and delicate hues which issue 
from this transparent light, as it is decomposed by the objects on 
which it falls. 

Theories respecting the Nature of Light, 

803. There has long been much dispute respecting the nature 
of light. The ancients Sisseried thdit there 7nust he sojnething be- 
tween the eye and the object seen ; for without sorde medium there 
could be no communication. The great question was to ascertain 
what this medium or this something was. One supposed " that 
ihe eyes themselves emit rays or emanations of some unknown 



■ Cause of several shadows of the same object. Cause of variety in colours 
of the ancients respecting the nature of light. 



Opinions 



320 NATURAL PHILOSOPHY. 

kind, by which distant objects are, as it were, felt." This hypo^ 
thesis was absurd, because it gave no reason why objects should 
not be seen as well in the dark as light, or in fact why there should 
be any darkness at all. Others imagined " that all visible objects 
are constantly throwing off in all directions, images, films, or 
spectral resemblances of themselves, which produce our impres, 
sions of the objects." Aristotle, in accordance with this opinion, 
supposed the mind to reside in the brain, Vv^hich was filled with the 
images, or forms of ideas as ivell as things, 

804. Newton, the great founder of the science of optics, reject- 
ing this idea of spectra, or resemblances being thrown off by the 
]-uminous body, supposed that particles of incalculable minuteness, 
dart in all directions from every portion of the surface of luminous 
bodies ; and that these particles are subjected to the laws of at- 
traction and repulsion. Possessing, as he supposed, these proper- 
ties of matter, he believed light itself to be material, and that its 
particles were turned aside so as never to come in actual contact 
with the particles of the bodies on which they fall ; but either be- 
ing turned back and refected by the repulsive forces before they 
meet them, as in the case of opaque bodies, " or penetrating be- 
tween their intervals, as a bird may be supposed to fly through the 
branches of a forest and undergoing all their actions, to take, at 
quitting them, a direction according to the position of the surface 
at which they emerge with respect to their course."* Newton's 
theory is called the system of emanation-, it being imagined that 
rays of light emanate from the sun, as water issues from a foun- 
tain. 

805. Another theory with respect to the nature of light seems, 
at the present day, to be in favour with many eminent writers. 
This supposes " light to be produced in the same manner as sound, 
by the communication of a vibratory motion from the luminous 
body to a highly elastic fluid," called ether, which fills all space. 
Thus instead of any thing being actually thrown off, this theory 
supposes light to depend on vibrations or undulations of ether, 
caused by that luminous body, as sound depends on pulsations of 
air produced by the sonorous body. 

There are strong objections to this theory. In the first place it 
supposes a substance, (ether,) v/hich we do not know to exists 
which supposition is contrary to the strict rules of sound philoso- 

* The learned Sir John Hcrschell, who is not a disciple of the Newtonian school, in 
respect to the nature of hght, tlius humorously illustrates Newton's doctrine of refraction ; 
but truth may he uttered in jest, and those who believe in the system of emanation, may 
rhank Sir John for his apt, and lively simile. 

Aristotle's opinion. Newton's theory. Theory of Vibrations. Objections to this theory. 



THEORIES RESPECTING THE NATURE OP LIGHT. 321 

jDhy ; and secondly its explanations of various phenomena of light 
are neither so simple nor so satisfactory as those of the Newtonian 
theory. Still there are analogies so close between sound and 
light, that there is some plausibility in referring them to analogous 
causes. 

806. One of the great advocates for the theory of vibrations, 
Euler, after asserting the existence of a subtle medium which per- 
vades all space, says, As the vibrations of air produce sound, the 
vibrations of ether produce light. The rays of light consist in the 
shapes and vibrations transmitted by the ether, as sound consists in 
the shakings or vibrations transmitted by the air. The sun then 
loses nothing of his substance* in this case, any more than a bell 
does in vibrating. Newton's theory of the reflection of light from 
opaque bodies, is thus commented on by Euler. " We see opaque 
bodies themselves, but not the images of the luminous bodies which 
enlighten them, as must be the case if we see them by the refrac- 
tion of their surface." 

807. Euler considers that an opaque body when illuminated, 
is in a state of vibration in its minuter particles, caused by the 

* The fears which some philosophers seem to entertain lest the sun will, in process of 
time, part with all its light, seems to shew but Utile confidence in the providence of Him 
who spalte light intV> existence; — why do we not fear lest the fountain of rivers will be 
dried, or lest the northern and southern portions of the globe will be left without an atmos- 
phere, since the air is continually rushing from thence towards the equator 7 We know 
that God has provided means for a constant renewal of the fountains by evaporation, and 
that there are in the upper regions of the atmosphere supplies of air going to restore the 
equilibrium. Thus the sun which bestows light upon all bodies within its system, may 
in return, by some process analogous to evaporation, draw from the opaque planets of its 
system, the elements of which light is composed, (for it is evident that light is a chemical 
combination of various elements ) Every where in nature we perceive a system of com- 
pensations ; the plant yields to the animal the vital element, and the animal in breathing, 
sends forth that substance which alone can give life and vigor to the plant. Shall we 
say, we do not understand how God can replenish the lamp he has set in the heavens, 
and therefore we will not believe his own assertion^ that he " gave the sun to rule the day 7" 
But the rather ad mit that every object which seems to reflect light is in motion, and that light 
itself is nothing but undulations of a supposed medium which all these vibrating objects 
put into motion. Instead of the sublime passage, " God said let there be light, and there 
was light," we should read, "and God said, let every thing begin to vibrate, so that there 
imay be an appearance of light." But we are met by another difficulty ; — at the period 
when the scriptures inform us light was created, there had been nothing else formed, and 
therefore there could be no vibratory bodies. We do not read in Holy Writ that God 
created sound, but we find sound in various places ascribed to the agency of air, and 
other media ; thus the expressions, a rushing wind, the sound of waters, etc. ; we do not 
indeed consider the Bible as a system of physics; there are manv sciences to Avhich this 
Holy Book has no immediate reference, but we think, that as ligl.t is plainly declared to 
have be^n created, a christian philosopher should not deny its actual existence as a prima- 
ry agent. 

Euler's remarks with respect to light and sound. Comments of Euler upon Newton's 
theory of light. 



322 NATURAL PHILOSOPHY. 

more powerful vibrations of the luminous body. " Opaque bodies,'* 
he says, " as long as they are not illuiiiinated, must be compared 
to musical instruments not in use, or to strings which emit no sound 
Till they are touched." Again he says with respect to colours, 
«• as in music, fiat and sharp notes depend on the quickness of vi- 
brations, a similar difference in the vibrations of the ra3^s of hght 
must produce as important an effect on vision. It is this effect 
which causes diversity of colours ; that is, difference of colour is 
to the organ of vision, what flat or sharp sounds are to the ear." 
Thus according to the system of vibrations or undulations, every 
simple colour depends on a certain number of vibrations which 
are performed in a certain time ; so that this number of vibrations 
made in a second produces that sensation which belongs to the red 
colour, another number of vibrations produces the sensation of yel- 
low, another of green, &;c. 

808. But we have wandered too long in regions of speculation. 
- It is our object to teach truth to the young ; facts that have been 

learned from observation, or may be demonstrated by experiment. 
Fortunately neither the theory o^ emanation, nor that o^ vibration, 
can overthrow the great doctrines of the science of optics, which, 
not being built upon the doubtful foundation of any hypothesis, 
need not of necessity stand or fall with it. We may add, too, that 
Newton's discoveries were explained in language consonant to his 
own peculiar opinions ; and that this language is still used even by 
those who reject those opinions. We shall therefore proceed to 
explain the nature of colours as first proved by this philosopher by 
means of the prism. 

Decomposition of Light. 

809. Light is not a simple substance, but the white light which 
comes fi^om the sun or any other luminous body, niay be decom- 
posed. 

Experiments to shew the compound nature of light are usually 
made with thei^mm. The optical prism is a triangular piece of 
glass, peculiarly fitted, by its shape, for refracting the rays of 
light. By means of such a prism, Newton proved that light con- 
sists of seven different kinds of rays, varying in colour, refrangi- 
bility, and other properties. His experiments may easily be 
repeated. Let -a room Le darkened, and admit a beam of 
light obliquely through a hole in the v/indow shutter. If this 

Opaque bodies compared to musical instruments. Colours accounted for on the system 
of vibrations. Leadiug doctrines of optics ftrraly established. Light, not a simple sub- 
stance. Optical prism. E.\-periments with the prism- 



SOLAR SPECTRUM, 



323 



Fi?, 260. 



beam of light be received upon a screen,* or upon the wall, a lu- 
minoLis spot only will appear ; or if a lens be placed before the 
beam of light, the rays will be bent out of their straight forward 
course, and in this refraction they will separate and arrange them- 
selves on the screen, according to their different degrees ofrefran- 
gibihty. The annexed figure will illustrate this experiment. 

E F represents the win- 
dov\^ shutter, H the hole, 
S the beam of light, 
which, without being in- 
terrupted would go on 
in a straight line and 
form a round white spot 
at P. B A C is a prism, 
whose refracting angle 
is at A. The beam of 
light fallinf? on its first 




'White '^'p 



surface C A emerges at 
an equal angle of refrac- 



tion, from its second surface B A in the direction g G. Now we 
should expect from the ordinary examples of refraction that this 
beam of light, which before fell upon P, would only change its di- 
rection and fall somewhere upon M N. But instead of a round 
white spot, there appears on the screen M N an oblong image K, 
divided into seven coloured spaces, of unequal extent, and arranged 
in the order represented, beginning with the red. This image is 
called the solar spectrum, or the prismatic spectrum. 

It will be seen t!iat the red ray is nearest the line P H, in which 
the light would have proceeded if it had suffered no refraction, 
while the violet is the most distant, from this line ; therefore the 
red ray is the least refrangible, and the violet ray the most refran- 
gible. The prismatic colours, as exhibited in the solar spectrum, 
are thus described by Thomson, the poet of the seasons, and of 
Nature. 



-; First the flaming red 

Sprang' vivicl jorth ; llie tawny orange next: 
Ami next delicious yellow ; by whose side 
Fell tiie kind beams of all-refreshing green. 
Tlien the pure blue, that swells autumnal skies, 
Etherial play'd ; and ttien of sadder hue, 
Emerg'd the deepen'd indigo, as wiien 
The heavy skirted evening' droops with fros% 

* Apiece ofwhite janer or the white wnll will serve the purpose of a screen, but a 

sheet of drawing paper fixed to a movable sliind is the ii;ost convenient. 



Colours exhibited in the sol ir spectrum. Order cf colours in thospectr.uu. 



324 



NATURAL PHILOSOPHY. 



While the last gleamings of refracted light 
Died in the fainting violet away. 

810. The various coloured rays of the spectrum may be col- 
lected by a convex lens, and when the image is received on a 
screen, a circular spot of white light is produced. Thus by syn. 
thesis, as well as analysis, is proved the compound nature of light. 
Pi?. 261. T\iQ,i the seven colours of the spectrum 

produce white light may also be proved 
by the following experiment. On a cir- 
cular card paint the colours in their due 
proportions, and on turning the card rapid,- 
ly, the coloured circle will appear white. 
It will be seen by the figure that the 
width of the violet ray is the greatest, 
being 80, and that of the orange the least, 
being but 27° ; green and blue occupy 
each 60° of the spectrum, yellow 48°, 
red 45°, and indigo 40°. 




Homogeneous Light. '■ — \ — 

811. It is asserted by some modern writers that there are but 
three homogeneous or simple colours, viz. ; red, yellow and blue. 
Orange may be made by mixing red and yellow, green by mixing 
yellow and blue, and violet seems but a faint shade of indigo, 
mixed perhaps with a little red. 

Sir David Brewster, one of the most popular writers on optics, 
of the present day, thus remarks upon homogeneous light. — 
" Among the wonders of science, there are perhaps none more 
surprising than the effects produced upon coloured objects by illu- 
minating them with homogeneous light, or light of one colour." 
After describing the method by which, owing to late chemical dis- 
coveries, yellow light may be produced in sufficient quantities for 
illuminating a room, he continues : " Having thus obtained the 
means of illuminating any apartment with yellow light, let the ex- 
hibition be made in a room with furniture of various bright colours, 
with oil or water coloured paintings, on the wall. The party which 
is to witness the experiment should be dressed in a diversity of the 
gayest colours ; and the brightest coloured flowers and highly 
coloured drawings should be placed on the tables. The room be- 
ing first lighted with ordinary lights, the bright and gay colours of 
every thing that it contains will he finely displayed. If the wfiite 



White light produced by collecting the pi ismatic colours. Remarks of Brewster upon 
homogeneous ligiit. Effects of illuminating objects with homogeneous light. 



HOMOGENEOUS LIGHT. 325 

lights are now suddenly extinguished, and the yellow lamps lighted, 
the most appalling metamorphoses will be exhiljited. The astonish- 
ed individuals will no longer be able to recognise each other. AH 
the furniture in the room, and all the objects which it contains, will 
exhibit only one colour. The flowers will lose their hues. The 
paintings and drawings will appear as if they were executed in 
Chinese ink, and the gayest dresses, the brightest scarlets, the 
purest lilacs, the richest blues, and the most vivid greens, will all be 
converted into one monotonous yellow. The complexions of the 
parties, too, will suffer a corresponding change. One pallid death- 
like yellow, 

like the unnatural hue - 

Which autumn plants upon the perished leaf, 

will envelope the young and old, and the sallow faces will alone 
escape from the metamorphosis. Each individual derives merri- 
ment from the cadaverous appearance of his neighbour, without 
being sensible that he is himself one of the ghostly assemblage. 

If, in the midst of the astonishment which is thus created, the 
white lights are restored at one end of the room, while the yellow 
lights are taken to the other end, one side of the dress of every 
person, namely, that 'next the white light, will be restored to its 
original colours, while the other side will retain its yellow hue. 
One cheek will appear in a state of health and colour, while the 
other retains the paleness of death, and, as the individuals change 
their position, they will exhibit the most extraordinary transforma- 
tions of colour. 

812. If, when all the lights are yellow, beams of white light are 
transmitted through a number of holes lilie those in a sieve, each 
luminous spot will restore the colour of the dress or furniture upon 
vv'hich it falls, and the nankeen family vv^ill appear all mottled over 
with every variety of tint. 

If red and blue light could be produced with the same facility, 
and in the same abundance as yellow light, the illumination of the 
apartment with these lights in succession v/ould add to the variety 
and wonder of the exhibition. The red light might perhaps be 
procured in sufficient quantity from the nitrate and other salts of 
strontian ; but it would be difficult to obtain a blue flame of suffi- 
cient intensity for the suitable illumjination of a large room. Bril- 
liant white light, however, might be used, having for screens glass 
troughs containing a mass one or two inches thick of a solution of 
the ammoniacal carbonate of copper. This solution absorbs all the 

Eli-jct orillaiiiiiuitiu^ with red and blue ligl't. 

28 



326 NATURAL PHILOSOPHY. 

rays of the spectrum but the blue, and the inter s'ty of the tlila 
light thus produced would increase in the same proportion as the 
white hght erapJoyed." 

Uispersion of Lights 

813. It is found that the length of the solar spectrum depends 
on the nature of the prism employed. Experiments a're made 
with transparent liquid substances of various kinds, enclosed within 
glass plates arranged in a triangular form. The oil of cassia^ 
when used as the material for a prism, forms a spectrum twice as 
long as the common glass prism. The former substance is there- 
fore said to have a greater disj^ersive power than glass. 

814. The difference between dispersion and refraction is wexy 
important. Newton himself, did not observe that the dispersion 
or divergence of the diiferent colours on the spectrum, was greater 
when produced by one refracting body than by another. He 
therefore erroneously concluded^ that the refractive and dispersive 
powers of bodies always corresponded. In the construction of his 
refracting telescopes he found much difficulty from the coloured 
fringes which rendered the image indistinct. Opticians have now 
learned to correct this defect, by the use of lenses of different dis- 
persive powers. Telescopes constructed thus are called achro- 
inailc.'^ The eye is an achromatic instrument. Its crystalline, 
aqueous, and vitreous humours, form lenses possessing differentdis- 
persive powers, which mutually correct the aberrations of each 
other. 

Rain-how. 

815. The rain-bow shows the prismatic spectrum on a gran^ 
scale, 

*' Bestriding earth tlie grand etherial bow 
Shoots up immense ; and every hue unfolds, 
In fiiir proportion, running from the red 
To where the violet fades into the sky." 

The raili-bow is caused b}'- the refection and refraction of light b;^ 
means of drops of water, which produce the effects both of convex 
mirrors and convex lenses. It is when the sun may be seen shi- 
ning through falling rain-drops thcit we see the rain-bow. If drops 

* From the Greek, a, destitute of, and krovia, colour. 

What is meant by the dispershig power of any reflocling substance ? Error of New- 
ton with respect to dispersion and reflection. Defects of Newton's telescopes. How re~ 
uiedied. Cause of the rain-bow. 



RAIN BOW. 



327 



Fior. 262. 




oi rain were flat instead of being round, the rays of light would be 
reflected by them to the earth without being divided into prismat- 
ic colours, and the rain.bow would appear an arch of glittering 
colourless light. But the spherical drops first bend or refract 
the rays dispersing prismatic colours, and then reflect them in the 
varied colours, and in the order they are exhibited in the prism. 

816. Suppose A to be a 
drop of rain, and S d a. ray 
of light falling upon it at d, 
it will not go to c, but be re- 
fracted to n, where a part 
will leave the drop, and a 
part be reflected to q, where 
it will suffer a second refrac- 
tion ; the drop acting as a 
prism, separates (disperses) 
the ray into the colours of the 
spectrum, the red being low- 
est and the violet highest, or^ 
m othei' v/ords, the red being least refracted, and the violet mos-i; re- 
fracted. The angle made by the red ray with the solar incident 
ray, that is the angle ^fq is about 42 degrees, v/hilethat made by 
the violet ray with the incident ray, or the angle S c q, is about 40 
degrees. It is in this way that the p?'imar]/ or principal rain-bow is 
formed by the united eflect of innum.erable rain-drops, each suffer- 
ing two refractions of light and one reflection. 

817. There are often seen tv/o bows, the one above the other, 
lainter, and with the colours in a reversed orxler. This is called 
the secondary rain- bow. The rays do not reach the eye of the 
spectator, until after two refractions and two reflections. Thus 
suppose the ray T r (see fig. 262.) to be entering the drop B at r; 
here it is refracted, (because it comes from air into water;) at s it 
is reflected to Z, where it is a second time reflected to u, where in 
leaving the water again for a nearer medium, the air, it is a second 
time refracted, and passses on towards g. The red ray is still 
nearest the inverted ray T r, and the violet ray is the most dis- 
tant. But a spectator at g would see the spectrum reversed 
in the secondary rain-bow. This is because the light enters al the 
lower pari of the drop and is transmitted through the upper. The 
secondary bow is also fainter, in consequence of the light which is 
lost by two reflections. 



Describe the rainbow. The secondary rain-bow. 



328 



NATURAL PHILOSOPHY. 




818. The arched ap- 
pearance of this phe- 
nomenon, is because the 
refracted rays are visi- 
ble to our eyes only at 
certain angles. Thus 
V^r£ if a line be drawn hori- 
-^^^ zontally from the eye of 
" the spectator, as E P, it 

r 13 evident that angles 

jrmed with this line, of 

^ I certain dimension in 

^l :very direction, will 

.^ ..,,, produce a circle. Sup- 

^^ iP pose three drops of rain 

^^^^-~--^^— ^ — ^-^ "^" only to be represented 

in the primary rain-bov/, it will appear that the angle C E P is less 

than the angle B E P, and that the angle A E P is the greatest of 

the three. This larger angle then is formed by the red rays, the 

middle one by the green, which is also the middle of the spectrum, 

and the smallest by the violet or extreme ray. 

Absorption of Light. 

819. The most transparent bodies in nature, as air and water, 
when in sufficient thickness, are capable of absorbing a great quan- 
tity of light. On the summits of high mounlcans where light has 
to pass through a less thickness of atmosphere, more stars are visi- 
ble than in the plains below. On looking up through a conside- 
rable depth of water, lumJnous objects are scarcely visible. The 
red colour of the morning and evenmg clouds is owing to the ab- 
sorption of the coloured rays by the air ; and the noonday sun 
when viewed from a diving bell in the depths of the sea, appears of 
the same hue. It is supposed that the light absorbed is stopped 
by the particles of the absorbing body, and remains within it in 
the form of impenetrable matter.* AUthe light that is not either 
absorbed or transriiitied is reflected, and the body assumes the 
colour of the reflected ray. 

820. There is reason for believing that there are certain rays 
of solar light which never reach us. For when a prism is very 
perfect, and the sun-beam is received on a white sheet of paper, it 

* Brewster's Optics. 



Cause of the arched appearance of the rain-bow. EfFrcts of the absorption of light. 
Is the colour of a body owing to light which is absoibed or reflected 1 



CONCLUDING REMARKS ON COLOURS. 329 

presents the appearance of a ribbon shaded with all the prismatic 
colours ; having its breadth irregularly striped by a number of 
hlack lines. These rayless lines are so narrow that they are scarce- 
ly visible without the aid of the microscope. But they are found 
always in the same part of the spectrum, and of the same propor- 
tional breadth. These vacant or rayless lines in the solar spec- 
trum are supposed to indicate the existence of certain rays which 
do not come to us. It is imagined that they may be ahsorhed by 
the sun's atmosphere. 

821. There are certain coloured flames, which when examined 
by a prism, exhibit spectra deficient in particular rays, like the 
solar spectrum when examined by coloured glasses. Pure hydro- 
gen gas burns with a blue flame, in which many of the other 
rays are wanting. Alcohol when mixed with water, affords 
no other flame but yellow. Most of the salts, when, in a powder- 
ed state, they are exposed to the blaze of a lamp, give colour to 
the flame as follows, to wit ; 

Salts of soda — homogeneous yellow. 
'* potash— pale violet. 
" lime — brick red. 
" strontia — bright crimson. 
" :^^0SSf^ — pale apple green. 
" copper — bluish green, 

822. Colour is not an essential property of matter ; bat it ari- 
ses from the action of matter upon light. Thus a v/hite cloth re- 
flects all tlie rays. But when dyed yellow, the particles of the 
cloth acquire the property of absorbing all the other rays, and of 
reflecting only the yellow. Bodies that reflect all the rays, ap- 
pear white ; those that absorb them all, appear black. Coloured 
bodies decompose light by absorbing some of the rays and reflect- 
ing others. The colour which a body seems to have, is in reality 
that for which it has no affinity, and therefore throws it off at its 
Surface, while the other coloured rays hide themselves among its 
particles. In the dark there is no colour, for there is no light to 
be decomposed ; therefore none to be absorbed and none reflected. 
So true is it, as expressed by the poet, that 

" Colours are but phantoms of the day, 

With that they're born, wiih that they tade away 

Like beauty's chamis, tlicybut amuse the sight, 

Dark in themselves, lill liy reflection l)rigiit , 

With tiie sun's aid, to rival liim they boast. 

But light withdi aw, in tlnir own shades are lost." 

. Black linrs in the solar spectrum; how accounted for 7 Ditlerent coluurcd ilaiurs^. 
How produced. Colour not an essential property of matter. Condvjdiug remarks uroH 
cclour. 

28* 



PART VII 



ELECTRICITY. MAGNETISM. 



LECTURE XXXIX. 



THEORIES OF ELECTRICITY MODE OF OBTAINING IT. CONDUCTORS 

AND NON-CONDUCTORS. ELECTRICAL APPARATUS, AND 

EXPERIMENTS ILLUSTRATING THE NATURE 

OF ELECTRICITY. 

823. From the mechanical laws which govern solids, we grad- 
ually proceeded to the investigation of liquids and of air ; and to 
the phenomena of sound connected with the latter. We have ex- 
amined the properties of light, that agent which, while it reveals to 
"US the forms of nature, is itself still a mystery confounding the wis- 
dom of philosophers, while it gratifies them by occasional discove- 
ries of new and unexpected properties. We are now to contem- 
plate another power in the machinery of the universe. One, 
"which, though it was unknown to man for thousands of years, is 
always present, around hini on every side, and appears connected 
with almost ail the physical changes which are taking place on the 
globe. This power is called electricity. 

824. Electricity is probably a material substance. But such 
is its subtle nature that i'ew of the properties common to matter 
have yet been discovered in it. Pervading the earth, its atmos- 
phere, and all terrestrial things, it neither affects their temperature 
nor enlarges their volume. When undisturbed it is quiet, giving 
no sensible tokens of its existence. But like the slumbering vol- 
cano, it is capable of being roused into action and exhibiting a 
terrific force. 

Retrospect of subjects considered. New subject considered. Electricitj' in its dor- 
mant state. 



GENERAL CHARACTERISTICS OF ELECTRICITY. 33 1 

825. Electricity was first observed as a property of amber, a 
resinous substance called in Greek, electron, from whence the name 
electricity was derived. Plato, and some other ancient writers, 
stated that amber, by rubbing, might be made to attract light sub- 
stances, as the load-stone attracts iron. The same property of 
attraction had been observed in jet, emerald, and some other pre^ 
cious stones. But all that was recorded by the ancients on this 
subject, was a few isolated facts and observations which seem to 
have excited litfle attention. 

826. It was not until the last century that electricity took its 
rank among the sciences. Our distinguished countryman, Dr. 
FrankUn, is acknowledged as the author of some of the greatest 
discoveries concerning the nature of this fluid, and especially its 
identity witii the lightning which flashes in the heavens. " To 
electricity," says Herschell, " the views of the physical inquirer 
now tm'n from almost every quarter, as to one of those universal 
powers which nature seems to employ in her most important and 
secret operations. This wonclerf d agent which we see in intense 
activity in lightning, and in a feebler and more diffused form tra- 
versing the upper regions of the atmosphere in the northern lights, 
is present probabi}'" in great abundance, in every form of matter 
whicli surrounds us, but lecomes sensible only when disturbed by 
experiments of peculiar kinds. Every body is familiar with the 
crackling sparks which fly from a cat's back when rubbed. These 
by proper management may be accumulated in bodies suitably dis- 
posed to receive them, and although then no longer visible, give 
evidence of their existence by a variety of extraordinary pheno- 
mena, — producing attractions and repulsions in bodies at a distances 
admitting of being transferred from one body to another under the 
form of sparks and Jlashes ; traversing with perfect facility the 
substance of the densest bodies called conductors ; producing pain- 
ful shocks and convulsive motions, and if in sufficient quantity, even 
death itself, in animals through v/hich they pass ; and fnially imi- 
tating on a small scale the effect of lightning. 

Such are. the general characteristics of the electric fluid ; and al- 
though we are about lo consider in detail some of its phenomeria, 
we have thought proper to introduce it to you in the concise de- 
scription of one of the ablest philosophers of this day. 'i'hus in 
meeting with a stranger there is an advantage in knov.ing tho 
general outlines of his character, though it is by personal acquain- 
tance only that we obtain a definite and satisfactory knowledge 
of it. 

Discovery of eloctriciiy. Elertricily (Irsl, rank"rd miior-g' tlic sciences. Geuoral elm- 
ruclenstics of electricity as expkiiiied by lieischell. 



332 NATURAL PHILOSOPHY. 

827. Though we make use of the term electric jluid, it must be 
landerstood that nothing more is implied than the unknown cause of 
electrical phenomena. Those who advocate the theory of a uni- 
versal etherial fluid, whicl) by its vibrations causes the phenomena 
of light, very naturally consider the electric fluid as intimately 
connected with it ; and as light and heat both usually accompany 
electrical experiments, we have reason to believe that they all re- 
sult from one source, but under different and complicated forms. 
Magnetism and galvanism are known to be produced by electrical 
excitement ; and chemistry refers to the same cause some of its 
most important changes. 

Explanation of Terms. 

828. Attraction is one of the most important properties of elec? 
iricity. On rubbing a glass tube with a dry silken handkerchief, 
it attracts light bodies, as down, silk, cotton and the like. 

When a body exhibits electrical appearances it is said to be 
excited. 

A body receiving electricity is said to be eleclrifxd. 

An electrified body is said to be insolated, when it is so situated 
that its electricity cannot escape. 

Conductors are substances which readily transmit the electric 
fluid ; non-conductors prevent its free passage. 

Glass and amber are both capable of electrical excitement ; but 
the electricity of the one, presents different properties from that of 
the other. The same difference is observed with respect to vari= 
ous other substances. The term vitreous electricity is applied to 
that Vi'hich appears on exciting glass and other analogous bodies, 
and the term resinous electricity is that which appears in amber^ 
sealing-wax and other resinous substances. 

Positive electricity means the same as vitreous ; and negative 
electricity the same as resinous.* 

Theory of Dr. Franklin. 

829. Doctor Franklin's theory of electricity is, that there is one 
electric fluid which exists in all bodies, and is naturally in a state 
of rest. That when the equilibrium is destroyed by friction or any 

* It is necessary that the pupil bear this fricl in raind; as tlie terms positive for vitre- 
ous, and negative for resinous, are used indiscriminately. 

What is understood by the term electric fluid? Atti action. Electrical excitement. 
An electrified body. Conductors and non-conductors. Electricity of glass and of arfr^ 
ber. Vitreous and resinous electricity. Positive and negative Uectricity. FrankliQ'f 
Iheory of electricity. 



MODE OF PRODUCING ELECTRICITY. 333 

Other exciting cause, one body becomes p 'us or posit IveJi/ electrified.). 
while the body in contact becomes minus or negatively electrified. 
Thus when a glass tube is rubbed with a piece of silk, the tube 
gains and the siik loses electricity. 

830- A theory of a different kind which was advanced in France 
previous to the time of Franklin's discoveries is now strongly ad- 
vocated. This theory supposes the existence of two antagonist 
electric fluids, called the vitreous and the resinous, from glass and 
resin, the two substances from which they are respectively produ- 
ced, which like an acid or an alkali neutralise each other. It is 
only when separated that they manifest their peculiar properties, 
and the most striking appearances are exhibited at the instant in 
which they unite. 

831. As either of these theories satisfactorily explain most of 
the electrical phenomena, it is not necessary to enter into a con- 
sideration of their comparative merits. The theory of Franklin 
has the advantage of simplicity. According to the analogies of 
nature we should not be inclined to attribute to two great agents 
that which could be effected by one ; and by an acknowledged 
rule in philosophy, " No more causes should be ascribed than are 
necessary to account for the phenomena. Some indeed assert that 
there are phenomena accompanying the transfers of electricity from 
body to body, and the state of equilibrium it affects under various 
circumstances, which appear to require the admission of two dis- 
tinct fluids, antagonist to each other, each attracting the other and 
repelling itself."* The terms positive and negative fltuids are some- 
timesused by the advocates of two fluids, and must be distinguish= 
ed from positive and negative electricity, which refer to the differ=. 
cnt states of the same fluid. 

Electricity is produced hy Friction. 

832. Exp. 1. Rub a piece of sealing-wax with a piece of silk, 
fur, or flannel, and it will have acquired the power of attracting 
substances. If a small pith ball be suspended by a silken thready 
a feather, or bit of cotton will be alternately attracted and repelled 
by the excited body. 

2. A sheet of white paper dried by the fire and rubbed briskly 

* HcrsclioU. 

Tlipor}' which originated in France. The studrnt nol (ibliii,'^d to adopt or rejccteitlicr 
theory. Wljy is Franklin's theory tiie more gimnlo? Positivo and nejjative flnids disi- 
tinguished from positive and negative electricity. E.\pci inanls which, show that cloolr".. 
city is produced by friction. 



334 NATURAL PHILOSOPHY. 

with Inciia rubber, will become so highly excited as to adhere to 
the table. 

3. If a glass tube be rubbed several times in the dark, and the 
finger be brought within half an inch, a spark will be seen between 
the finger and tube, accompanied by a snapping noise, and the fin- 
ger will, at the same lime, feel a sensation like the prick of a pin. 

These experiments prove that electricity is excited by friction, 
and that aitractioii, repulsion, light and sound are electrical phe- 
nomena. 

833. Bodies similarly ekdrijied repel, and differently electrified 
attract each other. If a bit of cotton, a feather, or a pith ball be 
electrified by touching it with an excited glass tube, it is then sup? 
posed to have the vitreous electricity, and if brought near a body 
which has the same kind of electricity it will be repelled, while it 
^yill be attracted by excited sealing-wax, or any other body, which 
contains the resinous electricity. 

Electrometer. 

834. The _pre5e?ice of electricity, its nature and quantity m^j 
be determined by a very simple instrument called an ehctrometer. 
The pendulum electrometer consistsof a glass rod fixed to a stand, 
and bent at the top. A thread of silk with a very small pith ball 

Fig. 264. attached to it is suspended from the glass hook. By 
means of this little instrument it is easy to determine 
v/hether the electricity given off by any substance is 
vitreous or resinous. When the pith ball of the elec- 
trometer is excited by glass, it will be repulsed by any 
body having the vitreous electricity ; and attracted 
by any body having the resinous electricity. On the 
contrar}'-, if the pith ball of the electrometer be excited 
,^ by sealing-wax, it will be repelled by the resinous, 

_^yjV^ and attracted by the vitreous electricity. 
r^-^iz:^— r^"?^ 835. Tlw two kijids of electricity are produced at 
the same time, the one kind in the hody rubbed, the other in the 
rubber. 

When a glass tube is rubbed with silk or flannel, as much posi^ 
tive electricity is excited in the glass, as there is negative in the 
silk. The kind of electricity depends on the substance rubbed. If 
dry flannel be rubbed against smooth glass, the flannel acquires 
the resinous, and the glass the vitreous electricity. When two 

Vitreous elpctricity communicated, and its effects upon bodies uhicli have the resin- 
ops ekctricity. Nature and use of t!ie electrometer. Effects upon the body rubbed and 
the rubber. On wliat does the kind i.f tlectricity depend ? How may any of the ten sub- 
stances named become positively, and how negatively electrified 1 



f\ 



CONDUCTORS AND NON-CONDUCTORS. 335 

plates of glass, one polished and the other rough, are rubbed 
against each other, the polished surface has the positive, and the 
rough surface the negative electricity. 

836. The following substances beconne positively electrified if 
rubbed with either of tliose nnentioned after them ; and on the con- 
trary, they become negatively electrified when rubbed with either 
of those named before them. 

1. Fur of a cat, 6. Paper, 

2. Polished glass, 7. Silk, 

3. Wool and flannel, 8. Sealing-wax, 

4. Feathers, 9. Rough glass, 

10. Sulphur. 
The fur of a cat, when rubbed against any of the bodies above 
named, affords the vitreous (positive) electricity. Sulphur, when 
rubbed against any of the bodies above named, affords the resinous 
(negative) electricity. Silk becomes negative when rubbed 
against paper, feathers, &c., but positive when rubbed against 
sealing-wax, rough glass, or sulphur. Thus when silk stockings 
have been worn over woollen, sparks and a crackling noise are 
often perceived on separating them. 

Conductors and Non-conductors of Electricity, 

83T. There is a great difference in the power of bodies to cod» 
duct or transmit the electric fluid. Among the conductors are 
the metals, charcoal^ living animals, fiame, smoke, steam, arid damp 
air. Among the non-conductors are resins, sulphur, wax, glass, 
silk, wool, hair, feathers, &c. Tiie air when dry is a non-cooduc 
tor, as are all vitreous and resinous substances. 

838. Bodies surrounded with non-conductors are said to be in- 
sulated, because when excited their electricity cannot escape. 
But when they are not insulated, the electricity is conveyed to the 
earth, which is a conductor, in order to accumulate electricit}^ 
•therefore, ihe excited substance must be insulated. If the air, as 
well as the earth, were a conductor, it would be very difficult to 
accumulate electricity. Damp air being a conductor, it is quite 
necessary to the success of experiments on electricity, that they 
be performed in dry weather, unless the air of the room be dried 
by artificial heat. 

Electrical Apparatus. 

839. The electrical machine is used in order to accumulate 
large portions of electricity, for the purj ose of experiment. 

Fnbstances reinarkabls as conductors or non-Ciiiiduclurs oreloclricity. An ii\siilalcd body. 



336 



NATURAL PHILOSOPHT. 




The figure represents what is 
termed a plate raachhie. This 
consists of a circular glass plate 
A, nearly two feet in diameter, 
turning upon an axis which pass- 
es through its centre. The plate 
is rubbed by two pairs of cushions 
B B. C, called the prime con- 
ductor, is a brass cylinder having 
tvro branches, so as to receive 
electricity from each cushion. 
E E are pieces of oiled silk pass- 
ing from the cushions near to the 
points of the conductor. F is the 
/landle by vvhich the plate is turn- 
ed. The cushions are stuffed 
with hair and coated with an 
amalgam Cuujuu.-_,c;d of tin, zinc and mercury, a substance which 
has been found to cause a great degree of electrical excitement 
when rubbed against glass. When the glass plate is made to I'e- 
volve rapidly, if the machine is properly prepared and the atmos- 
phere in a dry state, shocks and vivid flashes of hght will be seen 
passing over the surface of the glass, and from the cushions to the 
conductor. The light is supposed to be occasioned by the sudden 
compression of the air, owing to the escape of the electric fluid. 
Heat is also evolved, for gun-pov.'der, alcohol and other inflamma- 
ble bodies, are set on fire by the electric spark. 

840. The principles on which the electrical machine operates, 
are the following : 1. The rubber commAinicates with the floor by 
means of a metallic chain, which is a conductor of electricity ; 2. 
The floor com.municates with the earth, from whence are derived 
inexhaustible stores of the electric fluid ; 3. By the friction of the 
glass, positive electricity is acquired by the rubber, and this is 
attracted and carried off by the metallic points of the prime con- 
ductors, in v/hich it becomes accumulated. On presenting the 
knuckle to the conductor, a spark is seen, and a peculiar prickling 
sensation is felt. There is no greater mystery in this than there 
is in the pain we feel on touching a hot iron. In the latter case 
it is the passage of caloric into the hand which causes the sensa- 
tion ; in the former case it is the passage of electricity ; and we 
know no more what caloric actually is, than we do what electrici- 
ty is considered in relation to its essence. 



Describe- the electrical machine. Principles on wbich 
Cause of the seasatijn produced b\' ekctricity. 



;e electrical machine operates. 



ELECTRICAL APPARATUS. 



337 



841. If the communication between the earth and the rubber be 
cut off, the supply of electricity to the machine would soon be ex- 
hausted. 

842. The passage of electricity from one substance to another 
is termed induction. Active electricity existing in any substance 
tends always to induce the opposite electrical state in the bodies 
that are near it. 

843. By various experiments it has been found that electricity 
remains at or near the surface of bodies. It is found that in con- 
ductors of an elongated figure, the electric fluid is accumulated 
towards the two ends, and withdrawn more l^rom the central parts. 
Thus it is that electrical conductors terminating in a conical point, 
part with their electricity so readily. 

844. When the electric fluid is 
to be collected in large quantities for 
the purpose of experiments, a ves- 
sel, A, called the Leydenjar^ is made 
use of. It consists of a thin glass 
llllll jar coated internally and externally, 



Fior. 266. 




■conductor of the machine. 



to within about two inches of its 
mouth, with tinfoil. The accumu- 
lation of the fluid in this jar is called 
" the charge ;" this is effected by 
connecting the brass wire,with the 
knob at the top of it, with the 
When the electrical machine is work- 
ed, the fluid issues from it to the jar, rendering the inside positive- 
ly and the outside negatively electrified. 

845. This charge would remain for a short time, but would be 
gradually dissipated by the action of the air. But when it is de- 
sired to pass the charge through any substance, the discharging 
rod B is used. By applying one of the ends to the outside of the 
jar, and bringing the other up towards the knob communicating 
with the inside, an explosion takes place, and (he equilibrium be- 
tween the inside and outside of the jar is restored. The charge of 
a jar which v/ould contain a gallon is quite sufficient to fire gun- 
powder, or any other inflammable substance. A single spark will 
kindle spirits of wine or ether ; but when great intensity is rc- 



* So named from Leyden in Holland, the place where it was first constructed. 



Suppose the rubber to have no communication with the earth. Induction. Wliy con- 
ductors are of an elongated conical figure. Explain the construction of the Leyden jar, 
with the manner in wliich it is char:^od. Use ol the dischaiciii':;" rod. 



29 



338 



NATURAL PHILOSOPHY. 



quired, such as is sui^ 
ficient to fuse steel or 
other wires, deflagrate 
gold, or silver-leaf, 
&c., a comhination of 
jars, which may be 
all discharged at the 
same instant, is re- 
quired. This combi- 
nation is called the 
electrical lattery, and 
is usually constructed 
as in the figure. 



846. " An instrument called the spiral tube serves to ren- 
der the course of the electric matter visible, and shows its 
colour in a beautiful manner. One end of it is applied to 
the ball of the conductor, the other end being held in 
the hand ; the spark from the conductor instantly pass- 
es from one spangle of the tin foil, on the glass tube, to 
the other, and iDrilliantly illum.inates the v/hole. This 
experiment may be varied at the will of the operator ; 
and drawings or sketches of any kind may be laid down on 
plates of glass, and thus rendered luminous." 





plate j\, 



847. The eJecirophonis is a simple machine, 
consisting of an under plate or sole, B, covered 
with a resinous coat, and an upper plate or cover 
A, of metal or wood coated with tih-foil, and ha. 
ving a handle I, of glass or some non-conducting 
- substance. The resinous plate, being rubbed 
-S with a piece of fur, becomes charged with ne- 
gative or resinous electricity. The upper 
now placed upon the sole, or resinous plate, and the 



Electrical bnttoiy. S|,iral tisbe. Electrophorus 
mav be accumulaioJ v i:h it. 



id the maimer In which electricity 



ELECTRICAL APPARATUS. 



339 



finger being applied to the former, receives electricitVj which may- 
be transferred to a Leyden jar, by touching the knob. After re- 
peating this process several times, the jar may be found sufficient^ 
iy charged to cause a loud report on the application of the dis- 
charging rod, and to set fire to cotton. Although the negative or 
resinous electricity is first excited by rubbing the under plate with 
the far, the charge in the Leyden jar is of the opposite kind, viz-, 
the positive or vitrous. The fluid which is ohtained by induction 
heing always the opposite of that of the excited body. Thus, if in- 
stead of a plate coated with resin, a glass plate be used, the nega- 
tive or resinous electricity will be obtained. 

848. Electrical bells. The figure repre= 
sents four bells, a be d, hanging by brass 
rods, with a bell fixed on a brass pedestal 
A B, and four small brass balls suspended by 
silken threads. The brass rods which sus. 
tain the four balls, being connected with the 
prime conductor of the electrical machine, 
becoming electrified, attract the brass balls 
which hang by silk, and these acting as clap- 
pers cause a ringing ; the balls having gain- 
ed electricity by this contact with the bells, 
Hy off and are attracted towards the middle bell where they dis- 
charge themselves. They are now ready to be attracted again 
by the bells, which arc continually receiving new portions of elec- 
tricity from the electrical machine ; and thus the ringing of the 
bells may be continued as long as the machine is in operation. 

Fig. 271. 849. An insulating stool is a small foot- 

^^^^^^^^^^ ^tool with glass feet. A person standing on 
lii^^^^"^'^"'^^j this stool is said to be insulated, that is, there 

11 _^ -,v^^^^ is no medium' by which electricity can be 

||| ^ 11 conducted from him. If a person thus insu- 

11 ^ lated, hold in his hand a chain connected 

with the prime conductor, his body v/ill become a conductor, giv- 
ving off electrical sparks to substances presented to it, and attract- 
ing such as are sufficiently light ; his hair, which is similarly 
electrified, will rise and diverge in all directions, each single hair 
mutually repelling and repelled by the others. 




^m^ 



Isthechnrge in the Loyden jar of the same kind of electricity 7 
Eulating stool. 



Electrical bells. In- 



uo 



NATURAL PHILOSOPHt. 




850. Dancing figures illustrate in an amu- 
sing manner some of the properties of electri- 
city, particularly that of attraction and re- 
pulsion. Two metallic plates are represent, 
ed in the cut. The lower one is connect- 
ed with the floor. The upper plate being 
electrified by a communication with the prime 
conductor, attracts towards it light bodies. 
Let small figures, cut from some light material, 

such as pith, paper or the like, be placed on 

I^^^^H the lower plate ; on suspending the upper plate 
" " ^ at a little distance above them, they are at- 
tracted towards it. When the figures touch the electrified plate 
they acquire electricity, and are, of course, repelled by the upper, 
and attracted by the lower plate, now in an opposite electrical 
state. Discharging themselves by contact with the lower plate, 
they are again negative, and in a condition to be attracted by the 
positive plate suspended over them. Thus the electrified figures 
are alternately attracted and repelled by each other, as they are 
in opposite or similar states of electricity : and a very lively dance 
among the little excited images is thus kept up as long as the up- 
per plate continues to receive electricity. 

851. The light from the electric spark appears els u. pencil of rays 
or as a star, according to the species of electric fluid which causes 
it. A Leyden jar beijig charged with positive or vitreous electri- 
city, its outside coating is negative, or has the resinous electricity. 
Let the discharging rod, having its ends pointed, be presented, so 
that one of its points shall be within an inch of the knob of the jar 

A, and let the other point be as near 
to the outside coating of the jar ; the 
point C will be illuminated with a 
star, and the point B with a pencil of 
light. This is because the electric 
fluid, going from the inside to the out- 
side of the jar, (or making the elec- 
tric circuit) enters at the point C, and 
issues from the point B. But if the 
jar is electrified negatively on the in- 
_ side, the outside will then be posi- 
tive, and the electric fluid will pass from the outside to the inside 
of the jar ; the pencil of rays will then appear on the point C, and 
the star on the point B. The positive or vitreous electricity is 




Dancing figures, 
electricity. 



Light from the electric spark varies according to the species of 



ATMOSPHERIC ELECTRICITY. 341 

therefore designated by the pencil of rays which indicate the pas- 
sage of the fluid from the conductor, and the negative or resinous 
■electricity by the star which shews the fluid entering the con- 
ductor. 

852. The effect of electricity upon animals is so remarkable, 
that it is not strange, that when first discovered, it should have 
excited great attention ; and that many extravagant notions with 
respect to it should have prevailed. Men who had acquired some 
practical knowledge of the electrical apparatus, but who wore ig= 
norant of the philosophical principles which governed it, travelled 
about, astonishing the credulous, and deluding the sick, lame, and 
impotent with the fallacious hope that bj^ submitting to the process 
of " e/ec.'emi7i^," that is to receive a shock from a charged jar, 
they would obtain a certain cure for all their diseases. 

853. The animal system is a good conductor of electricity. If 
any number of persons join their hands, and the first in the circle 
presents a discharging rod to the outside coating of a charged.Leyden 
jar, at the same time that the last in the series touches with another 
rod the knob of the jar, thus forming an electric circle, a shock is 
felt throughout the whole circle, and by every one in it at the same 
-instant. If the jar is charged with positive electricity, the fluio^ 
will issue forth from the knob of the jar, and run through the cir- 
cle till it is discharged through the person who touches the outside 
coating of the jar ; but if the outside coating is positive, the fluid 
will pass in a contrary direction. 

So rapid is the motion of electricity, that it seems to be instanta- 
neous ; but like light it is doubtles progressive, though its velocity 
'is inconceivably great. 



LECTURE XL 



ATMOSPHERIC ELECTRICITI^ 



854. There is phvays more or less electriciiy in tlie atinosphere. 
This may be ascertained by experiments with a simple apparatus 
called the electrical kite. This has for a conductor a fine metallic 
wire twisted with the cord which forms the string. This conduc- 

EfFect of electricit)' upon auiuials. Electric ci;c!c. Mutioii of olccti iciiy. ElocKi- 
cal kite. 

29* 



342 NATURAL PHILOSOPHY. 

tor is insulated by being attached to a silken string. When this 
kite is raised in the atmosphere, the presence of electricity is mani- 
fested by the pith balls, or an electrometer connected with the 
lower end of the conductor or metallic wire. When the electri- 
city of the atmosphere is excited, as manifested by thunder clouds, 
there is much danger in thus daring to draw down the lightning. 

855. The electricity drawn from the clouds by the electrical 
khe, or a conducting rod, may be accumulated in a Leyden jar : 
and its properties are found to be the same as those of the tluid 
produced by the electrical machine. 

Doctor Franklin, observing the various electrical phenomena, 
was led, by reasoning from analogy, to believe that Hghtning resulted 
from the same cause. This theory he proved by experiments made 
with an electrical kite during a thunder storm. The following 
are some of the resemblances pointed out by this philosopher, be- 
tween electricity and lightning. 

856. 1, The zigzag form of lightning corresponds exactly iii 
appearance with a powerful electric spark passing through a con= 
siderable interval of air. 

2. Lightning most frequently strikes high bodies, as the sum<- 
mits of hills, high trees, towers, spires, chimneys, &c. So the 
electric fluid, when passing from one body to another, always 
seizes on the most prominent parts. 

3. Lightning and electric matter are both found to pass most 
readily those substances that are good conductors, such as metals, 
water, &c., and to avoid those that are non-conductors, as glass, 
silk, sealing-wax, resins, &c. 

4. Lightning inflames combustible bodies ; the same is readily 
effected by electricity. 

5. Metals aje melted by a powerful charge of electricity ; this 
is one of the most common effects of a stroke of lightning. 

6. Lightning fractures and disperses all brittle substances ; the 
same holds true with respect to the electric fluid. 

7. Lightning often produces blindness ; the same eflect is found 
to be pn.'duced on animals when subjected to a strong electric 
charge. 

8. Animal life is destroyed by lightning; strong discharges of 
the electric fluid will produce the sarne etfect. 

9. The magnetic needle is similarly affected by lightning and 
electricity, and iron may be rendered magnetic by both causes. 

857. The charging and discharging of electrics is a miniature 
representation of the sublime process which is going on in the 
heavens during a thunder storm. 

iNature of atmospheric electricity. Analogies between lightning and electricity. 



ATMOSPHERIC ELECTRICITY. 343 

Thus we have only to suppose a cloud to be positively electri- 
fied ; it will then draw towards it other clouds that are negati-vely 
electrified ; when these approach within what is termed, their 
striking distance, the fluid will dart from the positive to the nega- 
tive cloud ; the explosion will produce a loud report, which being 
echoed from cloud to cloud, will produce the roiling noise which 
Vie call thunder. It frequently happens that the lightning during a 
thunder storm, is seen darting from the clouds towards the earth, and 
there producing dreadful effects. This probably is the case, more or 
less, in most thunderstorms, and may be caused by the earth, over 
which the storm happens, being at the time negatively electrified. 

This natural operation 
of the electrical fluid is 
illustrated in the figure. 
The letter a represents 
^ a portion of the earth's 
surface ; c, the lower or 
non-conducting part of 
the atmosphere ; d, the 
clouds charged with 
J electricity ; g, g, the' 
" positive electricity of 
the clouds, met by the 
negative electricity, q, of the earth ; 7i, the point where the two 
meet, and where the explosion takes place. This explosion is of= 
ten very terrible, accompanied with intense lightning and astoun- 
ding thunder, often rending in sunder every thing that may hap. 
pen to be in the way of it. Buildings that are lofty are much ex= 
posed to its effects ; and hence the necessity of having conducting 
rods raised on them. These rods should be pointed at top, rising 
about six feet above the highest part of the building, and planted 
well in the earth several feet below its foundation. If a rod is in 
parts, connected together by loops or links, such links should be 
perfectly contiguous, that is, they should touch each other ; and 
when the rod is supported by fastenings to the walls of the building, 
it should be insulated, that is passed through a glass tube ; other- 
wise conducting rods might do more harm than good, by attracting 
the fluid to, and dispersing it through the building. 

858. Green trees being good conductors of electricity, those ri- 
sing high into the atmospliere are sure to attract the fluid towards 
them ; it is therefore highly dangerous to go under them for shel- 
ter during a thunder storm, as the frequent instances of its fatal 

Tliunder cloud. 




^44 NATURAL PHILOSOPHY. 

effects upon man and beast too often prove. The safest situation 
in the open air, in such a case, is at the distance of about fort)'' or 
fifty feet from trees or houses. Within doors, the middle of the 
room should be preferred, and such position might be rendered 
still more safe, by standing on a glass-legged stool, or hair mat- 
tress, or even a thick woollen hearth-rug. In a thunder storm the 
middle story of a house is considered the most secure, and the cel= 
lar the most exposed part of it. 

859. Thunder is supposed to be caused by the motion of the air 
rushing in to fill the void made hy the siidde7i j^assage of the electric 
fluid. Lightning is supposed to be caused by the sudden condensa- 
tion of the air, produced by the compressed force of the electric flu- 
id. The lightning is seen before the thunder is heard, because 
light travels faster than sound. 

Aurora Borealis. 

860. It is now generally believed, that the beautiful meteor, the 
Aurora Borealis or northern lights, is occasioned by the passage 
of electricity through the upper regions of the atmosphere, where 
tli,e air is some thousand times more rarefied than at the earth's 
surface. 

-_,. The figure represents a large glass tube fitted with a 

'^ brass cap at the top, from which projects into the tube, a 
wire terminating in a ball. At tb.e lower end of the tube, 
projects a similar wire, but pointed at the extremity. This 
tube, being exhausted by means of an air-pump, on ap- 
plying the electrical machine to it, the electric fluid will 
pass between the tv/o wires in a diffused luminous stream, 
having ali the characteristic appearances of the northern 
II lights. There is the same variety of colour and intensity ; 
the same undulating m.otion and occasional corruscations ; 
the streams exhibit the same diversity of character, at one 
moment minutely divided in ramifications, and at another 
beaming forth in one body of light, or passing in distinct 
^^^ broad flashes- 

861. The cause of the auroi'a borealis was long unknown. At 
present, philosophers agree in referring it to electrical agency. It 
generally appears in the form of a luminous arch above tiie nor- 
thern horizon, and extending from east to west across the heavens ; 
Ijut never from north to south. Those who witness the peculiarly- 
Safest situation in a thunder siorm. Caute of thunJer and lijrbtning. Aurora bore^ 

aiis, its connection with electricity. Experiment to s;.-ew the eflVct of electricity upon 
rarefied air. Supposed cause of the aurora borealis. 



MAGNETISM. 345 

soft and brilliant light produced by electricity in passing through a 
tube of highly rarefied air, cannot but be struck by its resemblance 
to the beautiful illumination of the aurora borealls, and will readily 
believe them to be effects of the same cause.* 

862. Though the name Northern Lights has been given to this phe- 
nomenon, the same luminous appearances are occasionally exhibited 
in the southern hemisphere. As such sublime displays of created 
effulgence are never made in vain, those polar accumulations of 
the electric fluid doubtless subserve some wise and conservative 
principle in the economy of nature. May it not be that, by this 
means, an electric circuit is formed between the equator and the 
poles, and the equilibrium in the earth's electricity thus maintained ? 



LECTURE XLI. 

MAGNETISM. 

883. Accustomed as we are to examine things by our various 
senses, it requires some faith to believe in the existence of matter 
which is neither manifest to the sight or touch. The electric 
jiuid, though neither tangible nor visible, yet in its effects is seen, 
heard and felt. Magnetism is a silent, invisible and intangible 
agent ; but we see its operations, and therefore we give credence 
to philosophers who assure us that these effects must proceed from 
some cause, the name of which they call magnetism or the mag- 
netic fluid. Would it not be very inconsistent, should these phi- 
losophers attempt to overthrow the christian's fjiith in the existence 
of God, on the ground that he has no sensible evidence of such a being ? 
A bar of iron attracts towards it a small bit of steel, this the phi- 
losopher says is caused by the power of magnetism. Must so sim- 
ple an effect be the result of a cause, and yet the universe itself 
exist uncaused ? Shall this regularity, order, and harmony of the 
creation be ascribed to accident, chance, or nothing, because the 

* The evening of January 25, 1837, was remarkable fur one of the most splendid ex- 
hibitions of this plienotnenon, which has been seen in our latitude. It can scarcely be ex- 
jiected that any persons now living will ever again see so sublime a display of" Almighty 
power in a similar form. 

Not confined to the northern liciiiit;plier(\ Suggestion with respect to the possible use 
of this phenomenon. Reflections suggested by the subject of magnetism. 



346 NATURAL PHILOSOPHY. 

philosopher has never seen the Power which created and upholds 
all things ; — because the power is not embodied and directly re- 
vealed in all its Ineffable Magnificence to the bodily senses of 
man ? 

864. This argument may to some appear unconnected v/ith the 
subject of our present lecture, but we think philosophy and religion 
have been too long disjoined, or rather have been viewed as entire- 
ly distinct, if not at variance with each other. The young need 
to have their faith in an unseen superintending providence strength- 
ened by various considei^tions ; and when in the course of their 
scientific pursuits, arguments leading to this end present them- 
selves, it is not to be counted as time lost if they pause to reflect 
upon them. 

865. We admit the existence of an unknown cause of certain 
phenomena which cause magnetism, and the bodies in which it 
operates are called magnets. 

The phenomena of magnetism are, 1. attraction and repulsion; 
2. the power of the magnet to impart its properties to other mas- 
ses of steel or iron ; and 3. its tendency to point towards the poles 
of the earth. 

868. A magnet may be either natural or artificial. The natural 
magnet is an oxide of iron, of a dark gray colour, very heavy, and 
with a metallic lustre. It has long been known as the load-stone. 
It is usually found in beds of iron ore, in irregular masses of a ^ew 
inches in diameter ; but sometimes in larger quantities. There 
are natural magnets of more than one hundred pounds weight, 
with the power of lifting two hundred pounds of iron by means of 
their attractive property. 

867. Every magnet has two opposite points called poles ; and 
at these points the attractive power is greatest. The poles are 

pj 276 called north and south poles, (see 

^ N and S in the figure) accordingly 

^ ^^^^^^^BS ~ ^^ s'as they point to the north or south 

pole of the earth. The imaginary 
straight line, N S, which joins the poles, is called the axis. 

868. If a magnet be immersed in iron filings, they will attach 
themselves to it, until it is completely covered. At the poles of 
the magnet the attracted filings will stand erect (as at figure 276 ;) 
but they gradually become less perpendicular, till, in the centre, 
they lie in a horizontal position. The curves thus formed are call- 
ed magnetic curves. 

Religion and philosophy not entirely distinct. JMngnetisgri — magnet. Phenomena of 
Eaagneiisin, Loadstone, Poles of the magnet. Iron filings attracted by a magnet. 



DIP OP THE MAGNET. 



34r 




869. The magnetic power, like electrici- 
ty, may be transmitted from one body to 
another. Thus by rubbing bars of iron or 
steel* with a magnet, an artificial magnet is 
formed, possessing all the properties of the 
natural one. Suppose a magnetised steel 
needle to be delicately made and exactly balanced upon a pivot, 
like that of the mariner's compass, so that it can move freely to- 
wards any point, it will not rest until its poles point nearly north 
and south. If this position is changed, the needle will vibrate un- 
til it settles in the same line as before. This is called the polarity 
or directive property of the magnet. 

Dip cr Inclination of the Magnet. 

870. The two poles of the magnet when at liberty to move free- 
ly do not lie exactly in a horizontal direction, but one pole inclines 
a little downwards, thus proportionally elevating the other pole. 
This is called the inclination or dip of the magnet. In northern 
latitudes it is the north pole of the magnet which is depiTssed, and 
the nearer the north pole the greater the depression. It is sup- 
posed that at the pole the needle would assume nearly a vertical 
position, its northern pole pointing perpendicularly downwards, 
and its southern pole upwards. At a point near the equator the 
needle has no dip ; but on proceeding towards the south pole of the 
earth, the southern pole of the needle begins to descend and th^e 
northern to rise, while at a point near the south pole the needle 
would assume a vertical position. 

Fig. 278. 



•/ 



/ 



\, 



\ 






871. Suppose N 
S to be a magnetic 
bar, whose north 
pole is N and whose 
south pole is S ; if 
a magnetic needle 
turning on a point 
were presented to 
the magnetic bar, it 
would assume the various positions of the arrow in the figure, n 
and s representing the north and south poles of tiie needle, and c 
the pivot on which it turns. It will be seen that the south pole of 
the needle points directly to the north pole of the magnet, and 



.\ 



* Steel isilie cariurct of iron, or iron coni'uined with carbo!" 



Artificial magnet. Po]arit3\ \Miat ia nieai.t by the dip of the magnet 1 



34S NATURAL PHILOSOPHY. 

the north pole of the needle to the south pole of the magnet ; as 
the needle is moved from either pole towards the centre of the 
magnet, the dip or inclination becomes less and less, untd at the 
centre it is horizontal. If the earth itself were a vast magnet, 
having its poles at some distance below the surface, the magnetic 
needle would shew the same inclination or dip as it does now. 
It was formerly believed that the magnetic attraction below the 
earth's surface produced this phenomenon ; but late observations 
by shewing the existence of circulating currents of electricity 
around the earth, have led to the opinion that this is the cause of 
the earth's apparent magnetism. If this hypothesis is true, it is at- 
traction from above, and not from below, that causes the dip of the 
poles of the magnetic needle. There are reasons to believe that 
the phenomena of magnetism are caused by opposite electricities ; 
in which case the poles of the magnetic bar and needle are attract- 
ed by the antagonist electrical fluids. 

872. That line around the earth where the magnetic needle has 
no dip, or maintains a horizontal position, is called the magnetic 

Fig. 279. equator. This does not coincide di- 

rectly with the earth's equator, but 
may be considered as a great circle 
surrounding the earth and inclined to 
its equator at an angle of about 12 
degrees. It crosses the equator at 

several different points, as represented in the figure by the dotted 

line. 

Deviation or Declination of the Compass, 

873. The magnetic needle, moving freely, does not pointdirectly 
to the poles of the earth ; this variation is called by mariners the 
declination or deviation of the compass. Although the deviation 
of the magnetic needle w^as known to some philosophers, two hun- 
dred years before the time of Columbus, yet it was not generally 
understood b}'' mariners. For Vv'hen the crew of that navigator, 
on his first voyage of discovery, learnt thit the needle of their 
-compass did not point directly to the pole, they were alarmed, and 
losing all confidence in that sure guide to the mariner, grew more 
mutinous towards their commander, through fear that he would 
never be able to conduct them back to their homes. 

874. There are methods of calculation by which due allowan- 
ces may be made for the variation of the magnetic needle, and the 

How is the subject illustrated. Magnetic equator, "What is meant by the deviatioa 
of the compass 1 




M 



LINES OF NO VARIATION. 



349 




^xact points of the compass ascertained. Thus suppose the line 
N S in the figure to represent the true meridian, or a line drawn 
due north and south, while that which is drawn at right angles 
represents the equator or a line from east to 
west. The magnetic needle does not fall on 
the meridian, as it would do if it pointed di- 
rectly to the north pole, but deviates from it, 
making the angle B O N, the line B O being 
15 degrees north. This shews the declination 
or deviation of the needle ; as this deviation 
north of the equator is towards the west, as 
seen at B, the decUnaHon is said to be 15 de- 
grees westerly. 

875. By the magnetic meridian is meant a vertical circle in the 
heavens, supposed to be drawn through a line in which the needle 
naturally places itself. This meridian does not, as we have seen, 
always correspond to the geographical meridian, though there are 
places in which the magnetic needle, freely suspended, points di- 
rectly to the poles of the earth, in which casethe meridians co- 
incide. 

876. Lines drawn on the globe through all places where the 
magnetic and geographical meridians coincide, or where the nee- 
dle points due north and south, are called lines of no variation. 
But such lines are themselves variable ; as the direction of the 
needle is not constant in the same place, but is subject to change 
through the influence of some unknown cause, 

877. In 1657, according to observations then made in London, 
there was no variation, the needle pointing directly to the north pole 
of the earth, and consequently coinciding entirely with the earth's 
meridian. After this period it began to vary a little towards the 
west. This variation continued progressively until 1818, when 
the angle of declination was 24 degrees 36 minutes west. Since 
then it has been slowly inclining towards the east. This devia- 
tion of the compass to the eastward and westward, seems to resem- 
ble the oscillations of a pendulum, which moving slovv'ly over an 
arc of many degrees of the earth's surface, should require some 
hundred years to go from one extremity of the arc to the other. 

878. To account for the phenomena of the declination of the 
compass, it has been supposed that there are magnetic poles con- 
stantly revolving, and that these poles do not coincide With the 
poles of the earth, except at very long intervals. Late observa- 
tioiis have rendered it probable that there are magnetic poles in 



M'thod of c;ilc\]lating iho variation oftlic needle. Majnetic meridian. Lines of no 
u-:ation. Line of no variation cliangiiief place. 

30 



350 NATURAL PHILOSOPHV. 

each hemisphere. One has been discovered in Siberia ; andRoss 
and Parry, in their late reports of discoveries in the polar seas, 
state that there is also an American magnetic pole, about 180 de- 
grees distant from that on the eastern continent. 

Theory of Magnetism. 

879. In observing the phenomena of magnetism we see no 
agent, v/e /icar nothing to inform us of its action, and we can leel 
or touch nothing v/hich gives evidence of its existence. But we 
do perceive the effects of the agent called magnetism. When we 
see filings of iron or a steel needle moving towards a bar of iron, 
neither impelled or drawn by any perceivable external force, and 
adhering with tenacity after they have come into contact, we per- 
eeive something for which we cannot account, otherwise than to 
refer it to the power of magnetism residing in the iron. We are 
more strucii with this* phenomenon, than with the attraction of 
gravitation, because it is less common ; and yet it is no more won- 
derfjlthat the needle sb.ould move towards the iron bar, than that 
the apple when loosed from the bough should move towards the 
earth. But while the attraction of gravitation is a universal prin- 
ciple, that of magnetism is confined to a very ^e\v substances, 
chiefly to iron and steel, and this limitation renders its operation 
still more mysterious. 

880. But though magnetism works in silence and obscurityj 
while electricity is attended by the flash, the thunder, and the 
shock, we have many reasons to believe they are different 
modes of operation of one and the came agent. 

1. Magnetism and electricity consist of two species ; the north- 
ern and southern* polarities, and the positive and negative elec 
tricities. •. 

2. These are governed by the same laws, viz., similar pov/ers 
repel and dissimilar powers attract each other. 

3. The magnetic influence is destroyed by the combination of 
the two polarities, and the electric action ceases on the union of 
opposite electricitif s. 

4. The force both of magnetism and electricity varies inversely 
[as the square of the distance. By comparing the number of vi- 
brations of a magnetised needle, during thesame time, at different 
distances from tlie magnet, it is found that the magnetic intensity; 

* Called also boreal (northern) and austral (sculhern) magnelisra. 

Magnetic poles of til 3 PEirth. ivTngneiism known only by its effects. Reasons for be- 
" liev.ngliiat magnetism and electricity aic the same agent. 



THEORY OF MAGNETISM. 351 

like ever}^ known force proceeding from a centre, diminishes with 
the distance, and as in the attraction of gravitation, in an inverse 
ratio of the square to the distance. A magnetic needle, being 
carried out of the direction in which it naturally rests, and left 
free again, vibrates in a manner similar to the vibrations or oscil- 
lations of a pendulum, until it has returned to its natural position. 
The greater the magnetic intensity which influences the needle, 
the greater will be the velocity of its vibrations, as the pendulum 
vibrates most rapidly, when most influenced by gravity. So it 
has been found by experiments that the force of electrieal attrac- 
tion and repulsion, varies inversely as the square of the distance 
from tlie excited substance. The reciprocal action of magnets 
and the electrical fluids are therefore subject to the laws of me- 
chanics. Four forces being in action, (that is two in each magnet, 
magnetic and electrical,) the composition and resolution of which 
are complicated, and offer a new and almost untrodden field of 
inquiry. 

5. Magnetism and electricity may both be communicated to 
other bodies by induction. But magnetism cannot, like electrici- 
ty, be transferred from one body to another. By induction is 
meant, that magnets and excited electrics communicate their pro- 
perties to other bodies in contact with them, by which process they 
are not themselves deprived of any portion of their magnetism or 
electricity. By the transfer of electricity is meant, that an elec- 
trified body gives off its electricity to another body. The pro- 
cess of induction is quiet ; while that of transference is accompa- 
nied by light and sound. 

6. The phenomena of magnetism, like those of electricity, have 
been explained on the supposition of one fluid existing in the state 
of plus and minus, or positive and negative ; and the contrary hy- 
pothesis of two analogous fluids. Those who advocate the hy- 
pothesis of one magnetic fluid, supposed that in the magnet, while 
there is a surplus at one end or pole, there is a deficiency in the 
other. The surplus or positive pole was said to be plus (or -}-) 
magnetic, and the deficient or negative pole was said to be minus 
(or — ) magnetic. This is according to Franklin's theory of elec- 
tricity. The theory of two magnetic fluids corresponding to the 
doctrine of the two species of electricity is now generally receiv- 
ed. According to this, in the particles of iron, and in all bodies 
in which iron is found, are lodged two fluids or forces, the one pre- 
dominating at one end, and the other at the opposite end, and that 
each particle attracts those particles* in which the opposite i\u\d 
prevails, and repels those in which a similar fluid resides ; and that 
this attraction and repulsion is with a force proportioned to the in- 
verse square of their mutual distances. 



352 NATURAL PHILOSOPHY. 

7. Lightning and aurora borealis, which are electrical phenome- 
na, are observed to have great power in disturbing the polarity of 
the compass ;* and it has recently been discovered by professor 
^Ersted of Copenhagen, that a current of volcanic electricity pro- 
duces similar effects. This discovery has given rise to the theory 
q{ electro-magnetism. 

881. "The connexion of electricity and magnetism," says 
Herschell, " had long been suspected, and innumerable fruitless 
trials had been made to determine the question. The phenomena 
of many crystallized minerals which become electric by heg,t, and 
develope opposite electrical poles at their extremities, offered an 
analogy to the polarity of the magnet so striking, that it seemed 
hardly possible to doubt the connexion of the two powers. The 
developement of a similar polarity in the voltaic pile pointed 
strongly to the same conclusion. Of all the philosophers who had 
speculated on this subject, none had so pertinaciously adhered to 
the idea of a necessary connexion "between the phenomena as 
aErsted. Baffled often, he returned to the attack ; and his perse- 
verence was at length rewarded by the complete disclosure of the 
vi^onderful phenomena of electro-magnetism. There is something 
in this which reminds us of the obstinate adherence of Columbus 
to his notion of the necessary existence of the new world ; and the 
whole history of this beautiful discovery may serve to teach us re- 
liance on those general analogies and parallels between great 
branches of science, by which one strongly reminds us of 
another, though no direct connexion appears ; and that such 
analogies are indications not to be neglected, of a community of 
origin." 

882. Though the connexion which exists between light and 
magnetism is obscure, its existence is certain. It had for many 
years been known that the violet ray of the solar spectrum has 
the power of rendering iron magnetic. In 1825, Mrs. Sornerville, 
an English lady distinguished for philosophical research, made a 
series of experiments by which she proved that the indigo, blue, 
and green raj's, as well as the violet ray, possess a magnetizing 
power. 

* At the time of the great aurora borealis of Jan. 25, 1837, the magnetic needle was 
observed to be remarkably disturbed. 

Herschell's remarks of experiments made to prove the nature of magnetism. Connec- 
tion between light and magnetism. 



MARINER'S COMPASS. 353 



Mariner^s Compass. 

883. The most important application of magnetism is found in 
the mariner''s compass. In order to trace the meridian b'ne which 
may point out the north and south, recourse may be had to astro- 
nomical observations, as the motion of the sun and stars determines 
tiiat direction. But the heavenly bodies are sometimes obscured, 
and in darkness and storm the mariner's compass is the only de- 
pendence of the seaman. Before its discovery long sea-voyages 
were not attempted; for if the mariner lost sight of the shore, 
he might wander far from his native land, with no pathway upon 
the trackless ocean to direct his return ; nor index to point 
out the proper direction. Like a blind man attempting to grope 
his way unaided to a distant city, he might be going in a di- 
rection opposite to the place of his destination. Without the aid ot 
the compass, Columbus might vainly have reasoned upon the exis- 
tence of another continent ; for with all his boldness he never would 
have dared to venture upon the untried ocean with no guide but 
the uncertain stars. 

884. The inventor of the mariner's compass is not known ; and 
it is even doubtful at what period or by what nations magnetic 
polarity was used for determining the direction of places on the 
earth's surface. 

It is supposed that a rude form of the compass was invented by 
the Tartars, to guide them in their wanderings over land ; and 
that tiiey imparted a knowledge of the instrument to the Chinese. 
The Crusaders on their return from the East brought it into Eu- 
rope, as they did many other valuable improvements in the arts 
and sciences, gleaned among the remnants of once powerful and 
enlightened nations. 

885. The compass first used was a very imperfect instrument, 
consisting of pieces of the natural loadstone fixed on cork or light 
wood, so that it miglit float on the surface of the water in a dish, 
on which were marked the cardinal points of the compass. In the 
compass now used, the magnetic needle is placed within a small 
box of brass, covered with glass, and so fixed as to retain a hori- 
zontal position in all motions of the ship. The needle is generally 
a thin, flat plate of steel, tapering towards each end, and to pre- 
vent friction, turning on the point of an agate, being one of the 
hardest of minerals, for a pivot. Beneath the needle is a circular 
card, on which are described two circles, one dividesd into 360 de- 

Ulility of the mariner's compass. Inventor of llie compass. First compass which 
was used. Compass now used. 

30* 



354 



NATURAL PHILOSOPHY. 



Fig. 281. 



grees ; and the other into 32 
equal parts called points of the 
compass ; of which the four, 
■yz2;., north, south, east, and west, 
are called cardinal points, while 
intermediate between these are 
the points N E or north-east, 
S E or south-east, S W or 
south-west, N W or north- 
west ; N b E is north by east, 
N N E is north of north-east, 
N E b E is north-east by north, 
&c. 
886. The surveyor's compass, used in surveying land, and the 
pocket compass, indispensable to travellers who wish to make their 
way through a pathless forest, are constructed upon the same prin- 
ciples as the mariner's compass, conveniently modified so as to 
suit the uses for which they are intended. 




-arveyor's compass. 



PART VIII 



CELESTIAL MECHANICS, OR ASTRONOMY. 



LECTURE XLII. 



INTRODUCTORY REMARKS. ARMILLARY SPHERE. IMAGINARY C1R=. 

CLES. TilE SOLAR SYSTEM. PLANETS. COMETS» 

APPLICATION OF MECHANICAL LAWS TO 

PLANETARY MOTION. 

887. Man is a being so transient in existence, so limited in 
faculties, and so blind to the designs of the Almighty, that it seems 
in no small degree wonderful that he should presume to scan and 
nneasure the objects by which he is surrounded. The child in re- 
garding the canopy of heaven, feels a mysterious awe and dread 
steal upon his spirit. He beholds that for which the surface of the 
earth around him has no parallel, and his feeble intellect becomes 
bewildered in the contemplation of the celestial glories. There is 
an idea prevailing among the ignorant and superstitious, that " it is 
wicked to count the stars." Though a small degree of mental 
illumination is sufficient to dispel such fear, there is yet connected 
with the study of the celestial bodies, a kind of awe, and a feeling 
that we tread on consecrated ground. Were science for the first 
time about to scale the heavens, and attempt to measure the mag- 
nitudes, determine the motions, and compute the distances of its 
luminaries, how bold and hopeless would seem the enterprise ! 
Should we not exclaim, " It is enough for us to learn something of 
the nature of the terrestrial objects around us, without presuming 
to understand the laws which govern the celestial spheres." 

888. But it is not left for the moderns to take the first steps in 
astronomy ; the ancients had much more correct notions of this 

Reflections on commencing the study of celestial mechanics. 



356 NATURAL PHILOSOPHY. 

science, than of the physical nature of the objects by which they 
were immediately surrounded. Man in the earliest ages was led 
to contemplate the heavens ; — the shepherds of the east, in their 
night watches on the plains of Babylon and Chaldea, made many 
important observations on the motions of the celestial bodies. 
A new star, seen by the wise men of the east, was a token to them 
that the Messiah v/as born, and following its guidance they travel- 
led westward, till the star stood over a little village of Judea called 
Bethlehem, " where the young child was." 

Anatomy was one of the branches of physical science which 
the ancients cultivated with most success. Notwithstanding their 
imperfect means of measuring time and space, they had l-jarned 
the motions of the sun and moon so as to be able to predict eclips- 
es with some degree of accuracy. The progress of astronomy 
was greatly impeded by the beliefia the doctrines of Aristotle, that 
the celestial bodies, in their mictions, were governed by laws pecu- 
liar to themselves, and bearing no analogy to those which regulate 
the motions of terrestrial bodies. But there v/ere those v/ho from 
■age to age attempted to throw off the chains which bound the in- 
tellect of man ; and faint glimmerings of light occasionally broke 
forth, shevi'ing the true pathway of science. 

889. But it was not until the time of Newton, that the motions 
of the heavenly bodies were explained, by the simple law "that 
every particle of matter attracts every other particle in the uni- 
verse, with a force proportionate to the product of their masses 
directly, and the square of their mutual distance inversely ; and 
is itself attracted with equal force." This law once established, 
what before seemed regularity without a plan, appeared a beautiful 
and harmonious system. Philosophers were ready to ask, " is 
this all ]" and to wonder that they had not before discovered what 
v/as so simple. 

890. The true mechanism of the heavens was nrst taught and 
proved by Newton. He not only established his theories by the 
most plain and conclusive arguments, but bringing mathematics 
to his aid, conclusively demonstrated the truth of his propositions. 

The pupil must not expect in these familiar lectures, designed 
to give but the outlines of philosophy, an attempt to explain all the 
phenomena of the heavens, or to make him acquainted with but a 
small part of the brilliant discoveries which illuminate the Princi- 
pia* of Newton, and the labours of his successors. 

* This is the title of Newton's work on natural philosophy; — to understand which 
has been called the test of a great mind. 
• — — — — ■ — ■ — ■ — — — - — ' 1 — 

Antiquity of astronomy. Impediment to its progress. Newton's laws of attraction. 
Newton's theory of the heavens. 



APPARENT MOTION OP CELESTIAL BODIES. 357 

891. Astronomy, though considered as a branch of natural phi- 
losoph}", is of itself a vast and comprehensive science; and there 
are at present many valuable treatises designed for a thorough il- 
lustration of the science. The object of this compendium is to 
impart to the young a knowledge of celeslial mechanics, by which 
we mean those mechanical phenomena of the heavens, which may 
be explained by a reference to the laws of motibn, attraction, and 
gravitation. By these well established laws and principles, the 
revolutions of the planets, and their satellites in their orbits, and 
their rotation on their axes, are all accounted for. 

Celestial mechanics may he defined, the science which teaches the 
magnitudes and distances of the heavenly bodies, their various mo- 
tions and other phenomena, and, the laws hy which they are gO" 
verned. 

892. When you stand in an open plain and look around, you 
perceive on all sides a circle where the earth and sky appear to 
meet. This circle is called the horizon. On looking upwards we 
see what appears a concave hemisphere. In the night it is span- 
gled with brilliant gems, many of which seem less than the dia- 
mond in a finger ring, while a body which seems much larger than 
any of the stars, illumines the earth with a mild but splendid light. 
In the day, all these lesser lights appear to have vanished, and one 
luminary with bright and piercing beams, alone is seen to move 
over the blue concave vault. 

But all these appearances are, in a degree, illusory. What 
seems to be the blue sky, is in reality only the body of air around 
us which decomposes the rays of light from the sun, and, absorbing 
all the other rays, reflects only the blue. The tiny twinkling star 
is in reality a sun, millions of times more vast in its dimensions 
than the world we live in. The moon which looks larger than 
any star, is in reality the smallest of all the heavenly bodies which 
are seen by the naked eye. But the moon is very near to the 
earth, in comparison with the distance of any other celestial body, 
and this makes it appear larger. But look at the moon through a 
powerful telescope, and you see as if within a short distance a very- 
large globe apparently suspended in air, and exhibiting on its sur- 
face the outlines of mountains, valleys, and even seas and vol- 
canoes. 

In the day, the stars are above us as much as at night; but as 
the glimmering of a candle is not perceived when we have the 
light of the sun, neither are the lesser lights of the heavens visible 
when that luminary is shining. 

What is understood by celestial mechanics ? Appearance of the lieavens. Difference 
between appearance and reality. Why the stars are not visible in ihc day. 



§5g NATURAL PHILOSOPHY. 

893. Again, the celestial bodies appear to rise in the eastern 
horizon, mount up to the meridian, and then sink in the west ; but 
it is in reahty our own motion, and not theirs, which causes these 
phenomena. And the blue vault is but an optical illusion. The 
stars, which seem set near each other in the etherial arch, are 
posted in various parts of infinite space, many millions of miles 
distant from us and each other, and are probably suns in the cen- 
tre of other systems of worlds. The body of atmosphere v/hich 
surrounds our globe, and through which rays of light from the ce- 
lestial luminaries penetrate, extends but about forty-five miles in 
depth. Beyond this v/e know not what may fill even the spaces 
between the globe of earth which we inhabit and the neighboring 
planets in our own solar system, ■ Some have imugined the ex-^ 
istence of a subtle fluid, called ether, whose vibrations produce the 
impression of light. Others suppose a fluid which, moving in cur- 
rents, impels the celestial bodies, and produces their various mo- 
tions. But we can never demonstrate the truth of these hypothe- 
ses, at least until some new discovery shall give us powers which 
we do not now possess. 

894. As the earth and its divisions are represented upon a 
sphere called the terrestrial globe, so the heavens are delineated 
upon a celestial globe, exhibiting the situation of the various clus- 
ters of stars which appear there. But the convex surface of a ce- 
lestial globe represents the apparent concave of the heavens, and 
therefore must fail to give us correct notions of actual appearan- 
ces. Some of the universities of Europe are furnished with celes- 
tial globes sufficiently large to admit several persons within. On 
the inner surface are painted the celestial bodies, and the various 
circles which astronomers imagine in the heavens. By the revo- 
lution of this artificial sphere, the spectators within see stars rise, 
ascend, and set as they appear to do in the real hemisphere. 

That point directly over head is called the zenith ; the point di- 
rectly opposite or underfoot is called the nadir. 

895. The fixed points round which the sphere of the heavens is 
supposed to turn, are the poles of the celestial sphere, or of the 
heavens, and a line drawn fromi one pole to the other, is called the 
axis of tlie heavens, and around this line the celestial bodies seem 
to revolve every day. 

Apparent motion of the celestial bodies. Cause of this apparent motion. Distance 
of the celestial bodies. Hypotheses of fluids beyond our atmosphere. Celestial globes. 
poles of the celestial sphere. Axis of the heavens. 



CELESTIAL GLOBES. 



85"§ 




y-t^' 



896. Suppose the earth 
to be within a revolving 
sphere,* as appears in the 
figure, and observe the 
various lines and circles 
which are here delineated. 

1 . The axis of the earth. 
This is an imaginary line 
passing through the earth's 
centre, and extending on 
each side to the poles of 
the celestial sphere. 

2. The meridian. If 
you point directly over 
head and move your fin=- 
ger towards the south pole, 
3^ou will describe a line 
which the sun crosses just 
at noon. This line is call- 
ed a meridian. Suppose 

so as to form a complete circle around 
the heavens ; it is evident that all the celestial bodies must cross 
this circle or meridian twice in twenty=four hours. The sun cross- 
es it at midnight as well as at noon ; and the star which v/e may 
see crossing our meridian at midnight, will at noon cross the meri- 
dian on the opposite side of the globe. The figuring on the meri- 
dian represents degrees. From the equator to each pole is one 
quarter of the celestial sphere or 90 degrees ; and no star can be 
more than ninety degrees distant from the horizon. 

3.. Equators or equinocilal line, is a broad belt encircling the 
middle of the earth from east to v/est, ttnd extending like a vast 
pi me to the sphere. 

4. Zodiac or elliptic, represents the sun's apparent path in the 
heavens, but tlie eai th's real path or orbit. 

5. Horizon ; this is an astronomical circle, called the rational 
or true horizon, and supposed to encompass the globe in the mid- 
dle,-. Icing 90 degrees distant from the zenith and the nadir. It is 
represented on the globe by a broad plane of wood or paper. This 
horizon is distinguished from the circle where the sky appears to 
touch tiie earth and sea. The latter is called the ssnsihJc horiz.n. 



ftuch a line extended 



This is called ihp arnvJlary sphere, from t!ie Latin, ariinlla, a bracelet, ring or circle. 



A.\:s of the caitli. Meridian. Equator. Zodiac. Ilorizoi, 



360 NATURAL PHILOSOPHY. 

6. The two colures ; these are two meridians which pass through 
the poles of the sphere ; they are called the equinoctial^ and sol^ 
stitial-\ colures, because one passes through two points in the- hea= 
vens, called the vernal and the autumnal equinoxes, shewing that 
when the sun in the echptic arrives at either of which, the nights 
are of the same length as the days ; and the other through two 
points called solstitial points ; because when arriving at either of 
those points the sun seems to remain stationar}'" for several days. 

7. Artie and antartic circles ; northern and southern polar cir- 
cles at a distance of 23 1-2 degrees from the poles. 

8. TrojJic of cancer and tropic of Capricorn, circles parallel to 
the equator at the distance of 23 1-2 degrees from it. 

897. The earth appears in the centre of the celestial sphere. 
In terrestrial globes the various circles which are delineated in the 
figure (fig. 282.) are usually marked on the surface, except the 
meridian, which is a brazen circle surrounding the globe, and 
dividing it into eastern and western hemispheres, and the horizon, 
which is a circular plane of wood dividing the globe into upper 
and lower hemispheres. By observing the ecliptic and other cir- 
cles drawn on the surface of the terrestrial globe, on a. map of 
the earth, the pupil often acquires erroneous ideas of them. 
The figure in which we have 'represented the astronomical cir- 
cles may rectify these notions. There is no real axis passing 
through the earth or the celestial sphere. The ecliptic or path 

"of the earth aruund the sun is assumed for astronomical pur= 
poses. The earth in its rapid motion around the sun, in reality no 
more leaves a track to mark its pathway, than the ship leaves its 
traces upon the pathless ocean. But yet for nearly six thousand 
years has the earth pursued one undeviating course, completing 
with perfect regularity its annual revolution. 

The cause of the planetary motions we shall consider afcer ha- 
ving made some observations on the celestial bodies which, in their 
united efforts upon each other, produce these motions. 

The Solar System. 

898. Astronomers suppose that the universe is composed of an 
infinite number of systems or families of worlds, each sun connected 

* Equinoctial, lilerally, signifies equal nights. 
t Solptiiial, liteiall)', signifies the sun stands still. 

Colures. Polar circles. Tropics. IManner in which the circles described are usually- 
represented on the artifiirial terrestrial globe. Danger of erroneous ideas. Systems cf 
worlds. 



PLANETS. 351 

with every other planet in its system or family, by ties that cannot 
be broken without throwing the whole into confusion. 

Of other systems than our own, little is yet discovered, though 
it is supposed that each fixed star is a sun, and the centre of its 
own system of worlds. 

899. Our system is called the solar system, and consists of the 
sun with its planets,* and their attendants called satellites or moons. 

The Sun. 

900. The sun is the centre of the solar system, and the source 
of light and heat, as well as the centre of attraction which connects 
the whole. Its magnitude is more than a million of times greater 
than that of the earth ; and it is ninety-five millions of miles distant 
from it. The sun was long supposed to be an immense globe of fire. 

"Some eminent astronomers of the present day believe it to be an 
opaque body surrounded by a highly luminous atmosphere. What 
the sun's real nature is we know not; but as its great Creator 
pervades every place throughout the universe, and yet has his seat 
in the heavens, so the sun, by his rays, is in all places throughout 
the solar system, while he is fixed in the centre of that system. 
The sun, like the earth, revolves on its axis, and completes one re- 

'ycliition in twenty-five days. This is proved by observing cer- 
tain remarkable spots on the sun's disc. These spots are seen to 
appear and disappear at regular intervals, which can o"nly be ac- 
counted for by supposing a rotation on its axis. 

The sun when viewed from any other system in the universe 
must appear as a fixed star docs to us. 

The Planets. 

901. Between the earth and the sun are two planets, Mercury 
and Venus. These are called inferior planets, because their or- 
bits are nearer the sun than the orbit of the earth, or, in other 
words, the}^ are v/ithin the earth's orbit. 

Mercury \s the most rapid in its motion of all the planets, and for 
; this reason was named by the ancient heathen after the swift mes- 
senger of the gods. 

Venus is, during one part of the year, Lucifer, or the morning 
star, and another portion of the year, Hesperus, or the evening 
star. She is the morning star when seen by us westward of the 

* Prom {he Gveck phut et2s, wandering or moviii:^. 



Si!ar isystcui. Magnifndi^ of the sun. Nature of the fc;nn. Kevoinfion of tl\e snn. 
Probable aj'iioaranco of lUc sua at clher pysteai.'^. luierior ])lanet3, IMii'raiiy. Venus. 



362 NATURAL PHILOSOPHY. 

sun, for she then rises before that luminary. She is the evening 
star when seen eastward of the sun, for she then sets after him. 
As the orbit of Venus lies between the earth and the sun, it follows 
that when she passes across the sun's disc, a dark round spot ap>. 
pears to us on that luminary. This is called the transit* of Ve- 
nus ; it has occurred only twice in about 120 years. The 
last that happened was the 3d of June, 1769. In the present 
century there will be two, one in the year 1874, and the other in 
1882. By the observation of this phenomenon many important as- 
tronomical calculations have been made. 

902. The earth is the third planet in the solar system. To an 
inhabitant of Venus our planet would appear much as she does to us. 
Looking on our earth as a star in the solar system, we are at once un- 
deceived as to the apparent motions of the heavenly bodies around 
it. Can we suppose that tlie vast orb of the sun, with the planets 
in its system, some of which are much larger than the earth, are 
all satellites to our little world ? Reason smiles at the supposition, 
and philosophy pronounces it impossible. The smaller bod}^, ac- 
cording to the principle of gravitation, and the laws of motion, 
must revolve around the larger. 

The 7noon is a satellite of the earth. Like the other heavenly 
bodies, it daily alters its apparent position, and in the course of a 
month, appears to make a complete revolution round the heavens, 
from west to east, while, at the same time, it has, like the fixed 
stars, an appai'ent daily motion from east to west. Among all 
the celestial luminaries, it is the nearest to us ; its mean distance 
being about 2B7,000 miles. V/hen the moon in her revolution in 
her orbit passes between the sun and the earth, the sun's light is 
partially or totally hidden from the earth, and this is calted an 
eclipse of the sun ; — when the moon falls into the earth's shadow, 
so that she is not enlightened by the sun, an eclipse of the moon is 
caused. 

* "90B. The ^plane's in the solar system whose orbits are beyond 
that of the earth, are called superior 'planets ; these are. Mars", Ju= 
piter, Saturn and Herschel, with four smaller, and lately discover, 
ed planets called asteroids. 

Mars has no satellite, and is known by his deep red colour. 

Jupiter is the largest of ail the planets, and is attended by four 
moons or satellites. Fie is distinguished in the heavens for his 
magnitude and brightness, being scarcely less bright than Venus. 

* Passing over. 

Transit of Venus. Tlie eaith considered as a star in the solar system. Tiie U)oon 
and her revolutions. .Superior pidnets. Mais. Jnpiter. 



cosiETS. . , 363 

When examined through a telescope his surface seems shaded by 
stripes. Some astronomers suppose these to be the effect of chan- 
ges in the atmosphere of the planet ; others that they indicate 
some great physical changes which are taking place on its sur- 
face. 

By the eclipses of Jupiter's satellites, light, which was tormerlj 
supposed to move instantaneously, is found to have a progressive 
motion. Also by observations upon these eclipses, with the help 
of optical instruments, the mariner niay determine the degree of 
longitude, when other means fail. 

Saturn shines v/ith a pale light ; he is attended by seven satel- 
lites and is remarkable for being surrounded with a double ring 
more luminous than the planet itself. This ring revolves around 
the planet, it is more than thirty-three thousand miles broad, and 
not quite three hundred miles in thickness, so that it resembles a 
broad plane. No part of its surface is nearer than about twenty- 
three hundred miles to the surface of the planet. From its great 
extent we may reasonably believe it to be a world of itself, and 
peopled with intelligent beings. 

Herschel, sometimes called Uranus,* and Georgium Sidus,* was 
discovered as late as ITS!, by the celebrated astronomer Dr. Wil- 
liam Herschel, who, with his sister Miss Caroline Herschel, and his 
son, Sir John Herschel, form a constellation of talent in the depart- 
ment of astronomy unrivalled, perhaps, by that of any other fami- 
ly. The planet Herschel is so immensely distant from this earth, 
as to be scarcely visible without a telescope. It has six moons 
or satellites. Beyond the orbit of Flerschet no planets have yet 
been discovered in the solar system. 

904. The asteroids revolve around the sun in orbits which are 
between the orbits of Mars and Jupiter. They are called Vesta, 
Ceres, Pallas and Juno. 

Comets. 

905. Comets are bodies which move around the sun in very long 
elliptic curves, sometimes approaching very near the sun, and then 
travelhng fir beyond the orbit of the most distant planet. Among 
hundreds of comets which have at different times been visible, the re. 
volutions of three only have been determined with any degree of ac- 
curacy. One of these, called Enke's comet, has a period of three 
years and 112 days ; it is very small and seldom visible to the na- 

* Uranus, in mythology, is tlie futlier ofSnturn. Gcnrgiuni Sidns, literally the Georgi- 
an star, yo named by Dr. liersche], in compliment to hid sovereign George III., Kuig ot" 
Great Britain. 

His satellites. Satarn. His ring. Hcrschell. When discovered. Asteroids. Comets. 



364 NATURAL PHILOSOPHY. 

ked eye. Another comet, which has a period of six years and 
three-fourths, appeared in 1822. Haliey's comet appeared in 
1835. The great astronomer whose name it bears, ascertained 
the period of its revolution to be about 75 years, sometimes a frac- 
tion of a 5'ear more and sometimes less. For the astronomer in 
computing the motions of comets, must take into the account, be- 
sides the usual rate of motion in different parts of their orbits, the 
delays which they may receive from the attractive forces of the 
various celestial bodies within Vv'hose spheres of influence they moy 
happen to fall. Thus Haliey's com.et, in one of its revolutions 
round the sun, vv'as delayed or retarded one hundred days, while 
within the sphere of attraction of the planet Saturn, and five hun- 
dred and eighteen days v/hile within that of Jupiter. 

906. Comets are accompanied by a train of light resembhng il- 
luminated hair,* called the tail of the comet. By some the comet it- 
self is supposed to be a nucleus of vapors, and the train or tail, which 
appears somewhat like the aurora horealis, to have its origin, as 
that meteor is supposed to have, in disturbed electricities. But 
nothing certain is known as to the physical constitution of these 
bodies. If comets are inhabited worlds, the beings who inhabit 
them must be fitted to endure the greatest diversity of climate ; 
from the burning heat of the sun when nearest to that luminary, to 
the total absence of heat, when traversing the distant and utmost 
boundaries of the solar system. They must endure also the change 
of being sometimes carried onv/ard with a velocity almost equalto 
that of a ray of light, and then the slow pace with which the com- 
et moves in the utmost point of its exceedingly eccentric orbit. 

Proporthnal Magnitude of the Planets. 

907. The earth is fourteen times as large as Mercury, very 
little larger than Venus, and three times as large as Mars. The 
diam.eter of Jupiter is 11 1-3 times greater than the diameter of 
the earth ; its surface is 118 times, and its bulk 1281 times great- 
er than that of the earth. The bulk of Saturn and his ring uni- 
ted is more than 1000 times greater than the earth. The sur- 
face of Herschel is nineteen times larger than the earth, but this 
planet is much less solid, so that its quantity of matter is only 
about seventy-eight times greater than that of the earth. 

Proportional distance of tJie Planets from the Sun. 

908. Mercury is thirty-seven millions of miles distant from the 

* Whence the name, from the Latin coma, a hair. 

Enke's comet. Conietof six years' [lerioci. Haliey's comet. Comet's train. Physi- 
cal constitution of comets. State the comparative magnitudes of the planets. 



ORRERY. 



36S 



sun. Next to Mercury is placed Venus, at a distance of sixty- 
eight mii lions of miles from the sun. Next stands the earth at 
the distance of ninety-iive milhons of miles from the sun. Mars 
is one hundred and forty-three millions ; Jupiter four hundred and 
ninety millions; Saturn nine hundred millions; and Herschel one 
thousand eight hundred millions of miles distant from the sun. 

That we may more easily comprehend the vast distances from 
the planets to the sun, some rule or measure adapted to the capa- 
city of our senses must be resorted to. As such, a cannon ball, 



moving at the rate of 
eight miles a minute, 
has been found conve- 
nient. With this velo- 
city a cannon ball would 
go from the sun to Mer- 
cury in nine and a half 
years, to Venus in eigh- 
teen, to the earth in 
twenty-five, to Mars in 
thirty-eight, to Vesta 
in sixty, to Juno in six- 
ty. six, to Ceres and 
Pallas in sixty. nine, to 
Jupiter in one hundred 
and thirty, to Saturn in 
two hundred and thir- 
ty. eigi it, and to Her- 
schel in four hundred 
and seventy-nine years; 
while it would go from 
the earth to the moon 
in twenty. three days'. 

909. By means of an 
orrery may be repre- 
senteci the motion of the 
planets around the sun, 
and thai of the satellites 
around the 'primary 
planets, with their com- 
parative magnitudes 
and. distances. 



Fig. 283. 




State the comparative distances of the planets from the suo. 

31* 



366 NATURAL PHILOSOPHY. 

On the upper plate, which answers to the ecliptic, are placed, in 
two opposite but corresponding circles, the days of the month, and 
the signs of the zodiac vvith their respective characters. By this 
plate the planetary balls may be set so as to be in their proper 
places on the ecliptic for any day in the year. A brass ball in 
the centre represents the san, this is supported by a brass rod which 
passes through the centre of the plate, and has sockets for sup- 
porting the arm.s by which the several planets with their satellites 
are supported. The planets are represented by ivory balls, ha- 
ving tiie hemisphere which is towards the sun white, and the other 
black, to represent their different phases. The moons or secon- 
diary planets are arranged in their proper order around the prima- 
ry planets. 

. By turning the handle of the orrery, a train of wheel- work, which 
is concealed in the circular brass box, under the upper plate, is set 
in motion. The planets revolve around the sun in the centre, and 
the moons revolve around the planets. To give a more perfect 
representation of the solar system, the planets with their respective 
moons, should have a rotary motion on their axes. 

910. Instead of a motion from east to west, which the celestial- 
bodies appear to have, ihey actually revolve around the sun, and 
upon their own axes, from west to east. The earth also revolves 
in the sam.e manner. This motion of the earth from west to east, 
makes the sun appear to us to move around us in a contrary di- 
rection ; as when you start from New York to go up the Hudson 
in a steam boat, the city itself appears to be moving southwardly, 
when in reality it is your own motion towards the north which 
causes this appearance. 

Application of Mechanical Laws to Planetary Motion. 

911. The attraction of gravitation is in proportion to the quanti. 
ty of matter. The sun being the largest body in the solar system, 
attracts the planets, and they in turn gravitate or tend towards the 
sun. 

912. Attraction decreases as the squares of the distance increase. 
Suppose a planet at B to be twice as far from the sun as at A ; then 

Fig. 284. 

f^h rm^ 



as the square of the distance 2X2 is 4, the attraction at B will be 

Explain the orrery. Real motion of the celestial bodies. Motion of the earth. Law 
of gravitation. The sun and planets mutually attracted. Decrease of attraction. 



ORBITS. 367 

four times less than at A, or \vhich is the same thing, the planet at 
A will be attracted with four times the force it would be at B. But 
if the distance of A from the sun \y eve four times less than that of 
B, then as the square of 4X4 is 18, the attraction at A would be 
sixteen times greater than at B. 

913. Since the planets are attracted towards the sun, with a 
force proportioned to his quantity of matter, and their respective 
distances, why, it may be asked, do they not fall upon the sun, as 
bodies near, and attracted by the earth, fall upon its surface? To 
solve this question, you will have occasion to recall what has been 
said of the effect of motion produced by two forces. Motion pro- 
duced by one force, you have learned, is in a straight line ; but the 
planetary motions, in their orbits, are circular. The planets do 
not fall upon the sun, because there is, in operation, another force 
besides that of gravitation which affects their motion. This is the 
projectile or centrifugal force, while the sun's attraction is the cen. 
tripetaJ force ; the joint action of these forces^ produce the circular 
motion of the planets, and keep them in their orbits. • Thus sup- 
pose a stone whirled round in a sling; here is circular motion re- 
sulting from two forces ; 1. the projectile 
force which was first given it by the arm, and 
2. the central force, or that with which it is 
held by the string. If the stone flies out of 
the string, the projectile force alone then act- 
ing, the stone will move from A to a, or in a 
tangent to the circle ; if let go at B, the stone 
will move in the tangent B b, or at C, in the 
tangent G c. 

914. By this law the moon moves round the earth, and the 
earth and other planets move round the sun ; the projectile force 
and the force of gravitation being so nicely balanced as to retain 
them in their orbits. Should one of these forces cease, the other 
would then act alone, the projectile force unbalanced, would carry 
the earth, in a straight hne, oif into infinite space; while the force 
of gravity alone would cause it to fall upon the sun. 

915. The orbits of the planets are not perfect circles, but el- 
lipses or ovals, that is, having greater length than breadth, and 
with two central points called i\\e foci. Suppose a planet. A, mo- 
ving by its projectile force towards B, if it met with no resistance 
it would forever move on in a straight line, and would pass in equal 

Circular motion of the planets, how pfoduccd. EH'ect of distnrbitig' eitlier of the two 
forces which keep the planets in their orbits. Elliptical orbits of the planets. 




368 



Natural philosophy. 



F\s. 2S6. 




^ times over equal spaces, that i3 
"^ from B to C in the same time as 
from A to B, and so on. But at 
B it is acted on by a new force, 
viz., the sun's attraction in the 
line S B. The two forces acting 
at the right angle A B S would, if 
equal, cause the planet to revolve 
in the circle B E F ; but the sun's 
attraction being more powerful 
than the projectile force, the plan- 
et is brought nearer the greater 
force, and describes the curve B 
G. Now at G the angle O made 
by the two forces is less than a right angle, in consequence of the 
forces acting more in concert, the motion in this part of the plan- 
et's orbit is accelerated, and further, as the distance of the planet 
from the sun decreases, attraction increases. At the point M the 
increased velocity has increased the centrifugal forqe so much 
that the planet would be impelled in a tangent towards D, were it 
not that the force of attraction is constantly becoming greater. 
Thus the motion of the planet is uniformly accelerated I'rom B to 
H. At H the projectile force is so great that it would impel the 
planet to I, while the attractive force would draw it towards S, 
but the joint action of the two forces carries it to L. In passing 
from H to B, or in going from the sun, its motion is retarded in 
the same degree that it was accelerated from B to II. 

The elliptical orbits of the planets are caused by a projectile 
force, and the continued action of gravitation, which draws the 
bud}^ from a true circle. 

916. A circle has within it a central point, which is equally 
distant from every part of its circumference ; but an ellipsis has 
tv»-o central points called focuses, or, more properly, ybc/. 

The sun (see preceding figure) is in the lower focus of the ellip- 
sis B GH. ^Vhen the planet is nearest the sun, as at H, it is said 
to be in its periliellon ; when most distant, as at B, in its aplie. 
lien. 

917. If the attractive powers of the sun were uniformly the same 
in every part of the orbits of the planets, they would pass over 
equal spaces in equal times. But on account of being more at- 
tractedin some parts of their orbits than in others, the planets pass 



E-xpluin the motion of a planet in its orhic Cause of the ellip'.ical orbit of the planets. 
Foci uf an ellirse. Perihelion. Aj^helion. Explain what is meaQt by the planets pass- 
ing over equal spaces in unequal times. 



FIXED STi^RS. 359 . 

over U7iequal porfinns of their orbits in equal timcT. But the m^^'io^^ 
which are included in those spaces are equal, that is, the ai-ea of 
the triangle B S W is equal to the area of the, triangle L S IT, al- 
though the areas which subtend these triangles are unequal. If 
the twelve triangles in the figure made by the lines proceeding 
from the circumference B M H to S be. considered as representing 
the twelve months in the year, you will perceive that the spaces 
through which the sun passes will be increased each month for 
one half of the year, and proportionably diminished the other half, 
though the areas passed over in each month are equal. It is one 
of the great laws of planetary motion, that the planets, in their 
revolutions, describe equal areas in equal times. 

918. The secondary planets in their revolutions round their 
primaries, are governed by the same laws as those which cause 
the revolutions of the primaries around the sun. Thus the moon 
being within the sphere of the earth's attraction, and acted upon 
also by a projectile force, is retained in her orbit and continues to 
revolve around the earth. The secondary planets move with their 
primaries around the sun. 

919. It is conjectured that the sun himself, with his retinue of 
eleven primary planets, and eighteen satellites, sweeps around 
some GRAND CENTRE tov/ards which solar systems gravitate as 
planets gravitate towards their centre ! But in pursuing such, 
suggestions, 

"Imagination's utmost stretch, 
In wonder dies avvoy." 



LECTURE XLIII. 

THE FIXED STARS. THE CONSTELLATIONS. GALAXY. NEEULAE. 

920. We have briefly noticed the bodies which compose the so- 
lar system, or that family of worlds with which our own is con- 
nected. But these are few in number compared with the whole 
glorious company of celestial bodies which we behold with the 
unassisted eye when looking at the heavens in a clear niglit. 

Revolutions of the secondary planets. Probable revolution of the whole solar system. 
Bodies in the solar system fev^r in comparison withllic whole number of stars seen by tha 
naked eye. 



0fO • NATURAL PHILOSOPHY. 

921. The planets shine with a steady light, \vhile the fixed stars 
are distinguished by their twinkling. The iigl.t of the mooil is 
more steady and mild tlian that of the sun ; the cause perhaps iS 
that the moon shines by reflected light, and the sun by its own 
powerful rays.. Now the pianets are all moons to us in respect to 
the reflection of light, but the fixed stars are supposed to be all 
suns, shining v/ith their own beams. The twinkling of the fixed 
stars is by some ascribed to the refraction and reflections produced 
by a variet}^ of atmospheres. The pianets seem as large or lar- 
ger than the fi.xed stars, because they are comparatively very 
near us. 

922. All the celestial bodies beyond our system are caWed Ji^jced 
£.tars, because they do not appear to change tlieir places in the 
heavens as the other planets do. This fixed appearance is proba- 
bly owing to their immense distance from the earth. The orbit of 
the earth is twice ninety-five millions of miles across, and we are 
therefore one hundred and ninety millions of miles nearer to some 
stats at one time than at another, yet they always appear to be in 
the same places; that is, the star which we see in the north is al- 
ways seen in the same latitude in the heavens ; that which we see 
at one time near the equator of the heavens, is always seen so, 
and that which we see in the south never appears in the north. 

923. If the circle A B represents the 
earth's orbit, the earth at A will be one 
hundred and ninety millions of miles nearer 
to the fixed star C, than it will be at B, and 
yet the magnitude of the star does not 
seem diminished bv this distance, nor 




i should we perceive any change in its posi- 
f tion, if in reality it were to move fro 



ity it were to move from C to 
D, because this change would be nothing 
in comparison to the distance of the star 
from the earth. Two stars which seenfi to 
us to be very near each other, may be millions of miles distant, or 
one may be far beyond the other in the depths of space. The ap- 
parent motion of the stars from east to west, is caused by the 
earth's motion on its axis. 

924. The fixed stars are supposed to be, like the sun of our 
system, centres of attraction around which revolve worlds with 
their attendant moons, and eccentric comets. These systems may 
be revolving in the immensity of space, but if so, our own is also 

Light of the fixed stars and planets. Fixed stars appear stationary. The cause of 
this appearance illustrated. Fixed stars supposed. to be suns. 



USE OF THE TELESCOPE. '^j\ 

pursuing the same round, and thus the relative positions of each 
are maintained. 

925. The stars have been arranged by astronomers according 
to their magnitudes and apparent brightness, into six classes. 
Thus Sirliis, or the dog star, is said to be a star of the first magni- 
tude. It is estimated by some very nice calculations of Dr. Wol- 
laston, that if this star were j>laced where the sun is, he would ap- 
pear to us three times as large as tlsat luminary, and give more 
than thirteen times more light. It is supposed that many of the 
fixed stars muet be miJHons of times larger than Sirius, These 
are calculations indeed which almost overwhelm the reason of 
man ! Tliey should teach us to humble that arrogance which 
seeks to find out "the hidings of Almighty power," and refuses 
to believe what human reason cannot comprehend, 

926. Stars of tb.e 5/a:^^ magnitude are the smallest which can 
be seen without a telescope They may in reality be much lar- 
ger than those that appear to lis of the first magnitude, on account 
of tlisir Immeasurably greater distance. 

92T. By the naked eye, only about tv/o thousand stars are vi- 
sible, though when v/e look at the heavens in a clear star-light 
night, their number seems beyond the power of computation. But 
this is an optical ilKision, arising from the countless reflections and 
refractions which light from the stars is subject to before it reach- 
es us. On looking at a star of the first magnitude, through a long 
narrow tube, the star will appear scarcely visible ; this shews that 
very few direct rays of the stars reach us, but that the brilliancy 
of ihe heavoLS is greatly owing to the reflection and refraction of 
light. 

923. The astronomical telescope hdiS revealed the heavens un- 
der a new aspect. . Our solar system has been enriched with new 
planets, the satellites and Saturn's ring have been discovered, 
and the moon's surface is found to be diversified by mountains and 
plains. 

Cni<=5es of st.irs acnnrdii!<r to rnagnifudc. Sirius. Stars of the sixth inno-niiude. 
. Nniiiber (if s nrs viriiblu to i!ie iiri\-ed PVR. Cause of their apj-cnriii^ more numeroin 
than they realiy are. Discoveries by laeans of the telescope. 



S72 



>JATURAL PHILOSOPHY. 



-^ ^'^- ^^^- 929. The figure represents 

^^^ a refracting telescope fitted up 

^^C ~ - for astronomical observations, 

^ "-:---. in the manner practised by as- 

tronomers. Suppose A A to 
be a large tube, into which is 
inserted the small brass tube 
D, containing the eye glasses. 
The object glass is fitted to 
the upper end of the large 
tube ; h k are two handles for 
adjusting the instrument, and 
i I are fbr the purpose of keep- 
ing it steady. 

930. In considering the 
subject of optics, we noticed 
the construction and operation 
of telescopes, and it is not ne- 
cessary to enter into particular 
explanations at this tim.e. The 
glasses, or lenses, are so form- 
ed that objects seen through 
them appear to be seen through 
a greater angle than when viewed with the naked eye ; this 
causes them to appear larger and nearer. 

931- Tha moon when viewed by the naked eye, appears und6r 
an angle of about half a degree ; therefore a telescope which rep- 
resents it under an angle of fifty degrees, magnifies one hundred 
times. 

932. "The first result of the invention of the telescope, and its 
application to astronomical purposes, by Galileo," says Sir John 
Herschel, " was the discovery of Jupiter's disc and satellites, — of 
a system offering a beautiful miniature of that greater one of whicli 
it forms a portion, and presenting to the eye of sense, at a single 
glance, that disposition of parts which in the planetary system 
itself, is discerned onlj^ by the eye of reason and judgment. We 
have here in miniature, and see at one view, a system similar to 
that of the planets about the sun." 

The Constellations. 

933. There has ever been in the mind of man a tendency to 
generalise and classify. Minerals, plants, and animals are group- 




Farts of the astronomical telescope. Why objects seen tbrongh the t'lescope appear 
magnified. The moon seen under an angle of fifty degrees. Y^'wri apjlicalion of the tel- 
jscope to astronomy. Tendency of mankind to form classes. 



ORION. 373 

ed together according to certain principles of resemblance. A col- 
lection of families is called a town, and many towns form a state. 
Even savages grouped themselves together in tribes; and follow, 
ing this bent of the human mind to generalise and classify, the 
priests ::nd learned men of ancient Egypt, under their serene and 
cloudless sky, and the ancient herdsmen and shepherds while tend- 
ing their flocks and herds by night, upon the plains of Chaldea and 
Babylon, observing the stars clustered together in groups, began 
to parcel out the heavens into various divisions, which they called 
constellations, and which they nam.ed according to their own pe- 
culiar fancies. 

934. In the book of Job, which' is considered one of the most 
ancient of the Holy Scriptures, the constellation Orion, and the 
Pleiades, are named, with " Arcturus and his sons." Orion is 
perhaps of all the constellations visible in a winter's night, in our 
hemisphere, the most brilliant and the most generally known. 
Not perhaps so well known by its scientific name, as by that of 
the yard and ell, and sometimes the three stars. Many a thought- 
ful youth has paused in his winter sports on the ice, to contemplate 
this grand constellation, as it spread itself across the eastern sky. 
In spite of the mirth of his noisy companions, his soul would be 
filled with enquiries as to the nature of those bright orbs, and the 
part they were fulfilling in the economy of the universe ! 

935. Orion is represented on the celestial globe, by the figure 
of a warrior, with a sword in his belt, a club in his right hand, and 
a skin of a lion in his left for a shield. He seems to defend him- 
self from the bull, the figure of which is represented in the con- 
stellation Taurus. 

936. Orion begins to appear in the eastern horizon, before nine 
o'clock in the evening in the early part of winter. Every evening 
he is seen higher and higher in the heavens, until the 24th of Jan- 
uary, his most northern star appears on the meridian ; the centre 
of the constellation is directly over the equator of the earth, and 
halfway between the poles of the heavens. Four bright stars in 
the form of a parallelogram form the outlines of the constellation. 
The two upper stars are considered as epauletts upon the shoulders 
of Orion, the western of the two lower stars is upon his left foot, 
the other upon his right knee. But what remarkably distinguishes 
this constellation, is the three bright stars in a row which form the 
heit of Orion, They are in the middle of the parallelogram ; and 
they are beautifully described in the book of Job, as the hands of 
Orion. " Canst thou loose the bands of Orion ?" inquired the Al- 



Orion. How represented on the celestial globe. Appearance of Orion in the heav- 
is. Principal stars in Orion. Bands of Orion. 

32 



374 



NATURAL PHILOSOPHY. 



mighty, of his presumptuous servant ! The three stars in the belt 
measure just three degrees in the heavens, and extend from north- 
west to south-east. 

937. In the head of Orion, is a triangle of three small stars, 
which form a large triangle with the tv/o in his shoulders. The 
two upper stars in the parallelogram are about 15 degrees north 
of the lower ones. The name of the star in the left foot on the 
west isRigel ; it is a star of the first magnitude, as is also the star 
on the east shoulder. The stars on the belt are of the second 
magnitude, those in the sword of the fourth and fifth magnitude. 

Fig. 289. 938. All that we have de- 

scribed of Orion, is plainly to be 
seen with the unassisted eye. 
But the telescope has revealed 
more than two thousand stars in 
this one constellation. One sin- 
gle star in the sword has been 
multiplied to twelve ; and in the 
belt no less than eighty stars 
have been discovered. Imper- 
fect as the best instruments are, 
and almost infinitely distant as 
is this constellation from us, how 
absolutely unlimited seems the 
number of stars which are clus- 
tered together in this neighbourhood ! A neighbourhood of stars 
of which the nearest are millions of miles distant ! 

939. The Pleiades, or seven stars, are a cluster which lie m 
the shoulder of Taurus, to the north-west of Orion ; they appear 
on the meridian a few minutes before 9 o'clock, on the first of 
January. The sun enters this cluster of stars in the spring, or 
season of blossoms, hence the inquiry of Job, " Canst thou bmd 
the sweet influences of the Pleiades?" In this cluster of seven 
stars, as seen by the naked eye, more than two hundred have been 
discovered by the aid of the telescope. 

940. The Hyades are in the head of the Bull, eleven degrees 
south-east of the Pleiades. The cluster is composed of five stars, 
so situated as to form the letter V. In this cluster is the red star 
Aldebaran, a star of the first magnitude. The constellation Tau- 
rus, or the Bull, is represented as only exhibiting the head and 
shoulders of the animal. 

941. The heavens are divided by astronomers, into three re- 




Triangle in the head of Orion, &c. Discoveries made by the telescope in the constel- 
lation Orion. The Pleiades. The Hyades. 



ZODIAC, 375 

gions. The northern and southern portions, and the Zodiac* 
The Zodiac, is a zone or girdle in the middle of the heavens, six- 
teen degrees broad, or eight degrees on each side of the ecliptic. 
The orbits of all the planets are within this zone. The ecliptic 
is the earth's orbit, or line described by the earth's annual revolu- 
tion round the sun. 

942. In ancient times, long before men had any true notions of 
astronomy, they supposed the sun moved around the earth, as in- 
deed on account of the earth's motion it appears to do ; and ob- 
serving that at different seasons, it appeared in different clusters 
of stars, they called these the signs of the Zodiac, 

Constellations in the Zodiac. 

943. The first astronomers seeing the sun always rise in 
March, with a particular cluster of stars, called this cluster the 
constellation Aries, (the ram ;) thus they said the sun is in Aries 
in March. In April the sun rose in another constellation, which 
they called Taurus, (the bull ;) and in May it rose in the constel- 
lation called Gemini (the twins.) These were the spring months ; 
and the names given to the constellations, were perhaps on ac- 
count of some fancied resemblance of their outline, to the objects 
after which they were called ; or from some relations of analogy 
connected with their agricultural or other pursuits, at the times 
when the sun successively rose with the twelve signs of the 
Zodiac. 

Thus the first signs, Aries and Taurus, are named after the 
animals which the shepherds and herdsmen, who were probably 
the first observers of the stars in reference to their influence upon 
the seasons, held in the highest esteem ; and the third might have 
been named in allusion to the twin season of their flocks. 

944. In this manner they parcelled out the Zodiac into twelve 
parts, or signs, each sign spread over thirty degrees of the heavens, 
or the twelfth part of three hundred and sixty degrees. 

945. This division of the Zodiac into twelve parts was arbitra- 
ry ; and although the constellations have somewhat changed their 
places, during the lapse of so many centuries, the signs still remain 
in the same order as numbered by the Chaldean shepherds ; but 
the signs do not answer to the same points ; and the stars, which 
were then in conjunction with the sun when he was in the equinox, 

* From the Greek Zodiakos, signifying an animal The 12 signs of (he Zodiac be- 
ing represented by 12 animals. 

The Heavens divided into different regions. Signs of the Zodiac. Signs which dis 
linguish the spring months. Why were these signs thus called 7 Twelve signs. 



376 NATURAL PHILOSOPHY. 

are now a whole sign, or thirty degrees, to the eastward of it ; so 
that the first star of Aries is now in the portion of the echptic call- 
ed Taurus ; and the stars of Taurus are now in Gemini, and those 
of Gemini in Cancer, and so on. By this retrograde motion, the 
pole, the solstices, the equinoxes, and all the other points of the 
ecliptic, have a retrograde motion, and are constantly moving from 
east to west, or from Aries towards Pisces, at the rate of about fifty 
seconds and a quarter each year, which is called the precession of 
the equinoxes. This rate of retrograde motion being constant, it 
will require twenty-five thousand seven hundred and ninety-one 
years for the equinoxes to make their revolutions westward quite 
around the circle, and return to the same point again. 

946. In June the sun enters the 4th sign. Cancer (the crab.) 
Here he ceases to advance northward, but begins to go back 
towards the equator. This retrograde motion might have sug- 
. gested the name of an animal which is said to move by going 
backwards. 

In July the sun enters the fifth sign, Leo (the lion ;) at v/hich 
time the heat of the sun was lion-like, that is, strongest and fiercest 
over the regions of Chaldea and Egypt. 

The sixth sign is Virgo, (the virgin,) represented as a female 
reaper. The sun enters this sign in August, the harvest month. 

In September, when the sun is in the sign Libra, (the balance,) 
the days and nights being equal, balance each other. This is the 
seventh sign. 

The sun enters the eighth sign, Scorpio, (the scorpion) in Octo- 
ber, when the autumnal fruits having engendered diseases, the 
season may be compared to the poisonous reptile which bears a 
sting in his tail. 

In November the sun enters the ninth constellation, represented 
by Sagittarius, (the archer.) The season when beasts of the chase 
are in flesh, and when men take delight in hunting. 

The tenth sign of the Zodiac, Capricornus (the goat,) is the 
emblem of the winter solstice, when the sun turns about, as it were, 
and, from the southern tropic, begins to climb towards the equator. 
The sun is in this sign six months after he has, like the crab, be- 
gan his retrograde motion from the sign or tropic of Cancer. 

The eleventh constellation on the Zodiac, is named Aquarius, 
(the water bearer.) It is represented by the figure of an old man 
in the act of emptying an urn of water. The season of humidity, 
fast hastening to its close. 

In February the sun rises with the constellation Pisces, (the 

Precession of the eqainoxes. Cancer. Leo. Virgo. Libra. Scorpio. Sagittari- 
us. Capricornus. Aquarius. Pisces. 



ZODIAC. 



377 



two fishes ;) indicating the fishing season, when the earth is bound 
in frost, the seas offer their stores for the sustenance of man. This 
is the twelfth sign of the Zodiac, and closes that great circle of the 
heavens. 

947. When the earth is in that part of her orbit represented in 
the figure at a, a right line from the earth to the sun, and extend- 



Fig. 291. 
Cancer. 



Leo. 9> 



Gemini. 



Virgo. im 



Libra. 



Scorpio. 1rt\) 




8 Taurus. 



T Aries. 



X Piices. 



Sagittarius. -^ 



Aquarius. 



Capricornus. 



ed to the fixed stars, would pass through the sign Libra, thus the 
sun would appear as if situated in that constellation. When the 
earth is at h, the sun will appear to be in the sign Capricorn. 

948. Besides the twelve constellations of the Zodiac, there are 
reckoned about thirty-five constellations in the hemisphere, north 
of that plane, and forty-five south of it. 

949. The Little Bear, (ursa minor) is a constellation situated 
near the north pole of the heavens ; from its being almost at the 
axis of motion, it scarcely has any revolution, and always ap- 
pears above the horizon. In this constellation is the North Star, 
sometimes called the polar star. It is a star of the third magni- 
tude, and not remarkably brilliant. 

The polar star is easily found by its being in the neighborhood 
of the constellation known commonly, as the Dipper.* Of this 

* The Great Bear, or Ursa Major. 



Explain what is meant by the sun being in any constellation. Number of constellations 
besides those of the Zodiac. Ursa minor. Polar star. 



378 



NATURAL PHILOSOPHY. 





Fig. 291. 






North Pole. 




1 


/^^^' 


(y /^ 


^^/"C^^K*/; 




\\)Jk 






^C// 


\\X 




P<<\> 


^V/ 


•4^ 


/^^L<1 V~' 




^ 



constellation, four bright stars form the bowl, and the three in the 
tail of the bear form the handle. The two stars opposite the 
handle are called the yointers^ because they always point to the 
north pole of the heavens, from which the polar star is nearly two 
degrees distant. Several degrees west of the dipper is a bright 
star of the first magnitude called Arcturus ; it is in the constella- 
tion Bootes, or the Bear Driver, so called because it seems to be 
pursuing the Great Bear around the pole. " Canst thou guide 
Arcturus with his sons, or bring forth Mazzaroth in his season?" 
enquired the Most High of Job. Arcturus here being the lead- 
ing star of Bootes seems to refer to the whole constellation. 
Mazzaroth is supposed to be a general term for the constellations 
of the Zodiac, which, by being brought forth in their respective 
months, cause the varieties peculiar to the different seasons. 

950. The study of the starry heavens is an elevating and noble 
pursuit, introducing us to a knowledge of God, by contemplating 
his most sublime and glorious works. From the earliest periods 
of time devotion has been warmed by it ; and poetry has received 
from it, its happiest inspirations ; Thus Euripides, in his drama 
entitled Ion : 

Meanwile the Night, robed in her sable stole, 
Her unrein'd car advances ; on her state 
The stars attend ; the Pleiades mounting high, 
And with his glittering sword Orion arm'd ; 
Above, Arcturus to the golden pole 
Inclines ; full-orb'd the month-dividing moon 
Takes her bright station, and the Hyades 
Marked by the sailor : &c. 

We hope no young person will feel indifferent to it ; but will make 



Arcturus with his suns. Mazzaroth. Remarks on the study of the stars. 



MILKY WAY. 379 

himself familiar at least, with the names and places in the most 
remarkable constellations and stars. It is as easy to find the 
place of Orion in the heavens, as it would Le to find the situation 
of St. Peter's church at Rome, or St. Paul's in London ; and as 
for " The Dipper," there are few children who have not had it 
pointed out to them. That brilliant star of the first magnitude, 
situated south and east of Orion, in the constellation of the Great 
Dog, called Sirius, or the Dog star, is always viewed with pleasure 
and delight, even by the vulgar and uninstructed. This beautiful 
star, although not often seen by us except in winter, is, in reality, 
over our heads during the day in mid-summer ; rising with the 
sun during a month, from the 24th of July to the 24th of August. 
The heat, which is usually most oppressive at this season, was 
formerly ascribed to the conjunction of this star with the sun. 
And so the distinctive name " Dog days^^ is still familiarly given 
to this season. 

951. The Milky Way, or Galaxy, is a luminous zone in the 
heavens, of a dazzling whiteness. It was long doubted by as- 
tronomers what occasioned this broad arch of light across the sky. 
But at length Sir William Herschel, aided hy his great telescope, 
proved that this brightness was the combined effect of myriads of 
stars, so distant that their image is lost to us. This celebrated 
astronomer counted not less than fifty thousand stars, which passed 
through the field of his telescope in a zone of the heavens two de- 
grees broad. 

952. NebulcE, are spots in the heavens, which even with or- 
dinary telescopes, appear but as white clouds, or masses of un- 
formed light. When examined by the best telescopes, they give 
the idea of a concave space filled with stars, insulated in the hea- 
vens, and constituting systems of their own. To attempt to count 
these stars, says Herschel, would be hopeless; but he tliinks 
many clusters of this description contain twenty thousand stars, 
compacted into a space not one tenth as large as the moon's ap- 
parent surface. " If each of these stars," says Mrs. Somerville, 
" be a sun, and if they be separated by intervals equal to that 
which separates our sun from the nearest fixed stars, the distance 
which renders the whole cluster scarcely visible to the naked eye, 
must be so great, that the existence of this splendid assemblage 
can only be known to us by light which must have left it at least 
a thousand years ago." 

Having indulged imagination in wandering through the solar 
system, and the more remote regions of space, as far as the human 
intellect has yet dared to penetrate, we must now return to our 

Galaxy. Nebulae. 



380 NATURAL PHILOSOPHY. 

own little planet. — The earth, indeed, appears insignificant, when 
considered in relation to this vast universe, and even to the sys- 
tem of which it forms a part. Among the family of worlds which 
move around the common centre of attraction in the solaj system, 
our planet is but an inconsiderable member. If Mars and Mercu- 
ry are of less magnitude, the far distant Herschell, with his 
numerous satellites, Saturn with his splendid ring, and attendant 
moons, and the magnificent Jupiter with his retinue of worlds, all 
fill a far greater extent of space, and must offer to the view of a 
spectator situated in some central point, an appearance far more 
grand and imposing than earth with her diminutive size, and the 
one little ball which revolves around her. Let us learn a moral 
lesson from the stars ; — we see that God has not made them all 
alike, but "that one star differeth from another star in glory," yet 
each harmoniously fulfils its destined round in the economy of na- 
ture. So it is with us, the beings who inhabit the little planet, 
called earth. Some have more wealth than others, some have 
greater intellectual power, some are lifted up, and some cast down ; 
b'lt all should harmoniously move on in their assigned orbits, trust- 
ing that he who placed them there, knows best how to order his 
own creation.' And again, there are always some compensations, 
which may be set off" against disadvantages — thus the earth, though 
more humble than Jupiter, receives more warmth and light from 
the fountain of light and heat ; and the lowly man is often pecu- 
liarly favored with spiritual enjoj-ments, and the light of God's 
countenance. 

But our connexion with the earth we now inhabit, is of short 
duration ; — we move upon it for a little while, and then our ashes 
will repose in its bosom until that day, " when the heavens will be 
rolled together as a scroll, and the earth shall melt with fervent 
heat." Under new and glorious forms, we shall then be transla- 
ted to regions free from sin and sorrow ; our celestial bodies will 
have power to range through the infinity of creation, and our souls 
will be delighted in the contemplation of glories which mortal eye 
hath not seen. But that we may be thus happy, thus blessed, we 
must here cultivate the better faculties of our nature ; we must 
make our intellectual attainments subservient to moral elevation ; 
the truths of science should be collected into one focus, to warm 
and animate the heart, so that God, the author of nature, may be- 
come the supreme object of our affections. 



WP 1 7 1Q/tQ 












,^ ^ 



.'^ ;^ ^ 






r °-.- '•. 






/ '* 










r>:% 






<d- <?^ 



.<^m;=%,# /^^*V\f ;'S^°\"''' 













95 " 














^^ o^ .'"^ICa 






^ V 
^ 

.^^ 









% .A^ 



v^ 



- "^^^^' 






< 



'^^ 






.. V : . . „ ,. \'" ;t:- ;,r ^ „ ,^ o^'.::«5^.y 













.<i> 






\^v^^ -k 







.'^\^-», <^ 



''^^i/K 



^ 



"^^^ •<; 












